Tootfinder

High-Dimensional Statistical Process Control via Manifold Fitting and Learning
Burak I. Tas, Enrique del Castillo
https://arxiv.org/abs/2509.19820 https://…

High-Dimensional Statistical Process Control via Manifold Fitting and Learning
We address the Statistical Process Control (SPC) of high-dimensional, dynamic industrial processes from two complementary perspectives: manifold fitting and manifold learning, both of which assume data lies on an underlying nonlinear, lower dimensional space. We propose two distinct monitoring frameworks for online or 'phase II' Statistical Process Control (SPC). The first method leverages state-of-the-art techniques in manifold fitting to accurately approximate the manifold where the data resi…

Staying on the Manifold: Geometry-Aware Noise Injection
Albert Kj{\o}ller Jacobsen, Johanna Marie Gegenfurtner, Georgios Arvanitidis
https://arxiv.org/abs/2509.20201 https://

Staying on the Manifold: Geometry-Aware Noise Injection
It has been shown that perturbing the input during training implicitly regularises the gradient of the learnt function, leading to smoother models and enhancing generalisation. However, previous research mostly considered the addition of ambient noise in the input space, without considering the underlying structure of the data. In this work, we propose several methods of adding geometry-aware input noise that accounts for the lower dimensional manifold the input space inhabits. We start by proj…

Geometric Building Blocks of Effective Field Theory Amplitudes
Timothy Cohen, Xu-Xiang Li, Zhengkang Zhang
https://arxiv.org/abs/2509.20449 https://arxiv.o…

Geometric Building Blocks of Effective Field Theory Amplitudes
On-shell amplitudes are invariant under field redefinitions. Nonderivative field redefinitions have a natural interpretation as coordinate transformations on the target manifold. General field redefinitions, which may involve derivatives, can be viewed as coordinate transformations on the field configuration manifold. We present a unified perspective for the geometry of both the target manifold and the field configuration manifold for scalar effective field theories. In both cases, we identify …

Homogenization and 3D-2D dimension reduction of a functional on manifold valued BV space
Luca Lussardi, Andrea Torricelli, Elvira Zappale
https://arxiv.org/abs/2507.18390 https:…

Homogenization and 3D-2D dimension reduction of a functional on manifold valued BV space
We study the simultaneous homogenization and dimension reduction of an energy functional with linear growth defined on the space of manifold valued Sobolev functions. The study is carried out by $Γ$-convergence, providing an integral representation result in the space of manifold constrained functions with bounded variation

An example of path integral reduction for a simple symmetric mechanical system on a product manifold
S. N. Storchak
https://arxiv.org/abs/2509.19527 https://

An example of path integral reduction for a simple symmetric mechanical system on a product manifold
A path integral reduction procedure in Wiener-type path integrals, based on the approach developed in arXiv:1912.13124, is applied to a simple invariant mechanical system defined on a product manifold with a given free, proper and isometric action of the group SO(2). The Jacobian of the path integral reduction and the integral relation between the path integrals representing the fundamental solutions of the parabolic equations on initial and reduced manifolds are obtained.

Curvature at the infinity of asymptotically flat Einstein manifold
Bing Wang, Hao Yin
https://arxiv.org/abs/2508.16288 https://arxiv.org/pdf/2508.16288

Curvature at the infinity of asymptotically flat Einstein manifold
In this paper, we construct coordinates at the infinity of an asymptotically flat end of a Ricci-flat manifold $(M_m, g)$ as long as the $L^{m/2}$ norm of the curvature is finite in this end. As applications, we can define a Weyl tensor at the infinity of $M$ and a version of renormalized volume following Biquard and Hein to ALE Ricci-flat manifolds/orbifolds of any dimension.

The metric compactification of a Kobayashi hyperbolic complex manifold and a Denjoy--Wolff Theorem
Vikramjeet Singh Chandel, Nishith Mandal
https://arxiv.org/abs/2507.18156 http…

The metric compactification of a Kobayashi hyperbolic complex manifold and a Denjoy--Wolff Theorem
We study the metric compactification of a Kobayashi hyperbolic complex manifold \(\mathcal{X} \) equipped with the Kobayashi distance \( \mathsf{k}_{\mathcal{X}} \). We show that this compactification is genuine -- i.e., \( \mathcal{X} \) embeds as a dense open subset -- even without completeness of \( \mathsf{k}_{\mathcal{X}} \), and that it becomes a \emph{good compactification} in the sense of Bharali--Zimmer when \((\mathcal{X}, \mathsf{k}_{\mathcal{X}}) \) is complete. As an application, w…

Riemannian Optimization for LoRA on the Stiefel Manifold
Juneyoung Park, Minjae Kang, Seongbae Lee, Haegang Lee, Seongwan Kim, Jaeho Lee
https://arxiv.org/abs/2508.17901 https:/…

Riemannian Optimization for LoRA on the Stiefel Manifold
While powerful, large language models (LLMs) present significant fine-tuning challenges due to their size. Parameter-efficient fine-tuning (PEFT) methods like LoRA provide solutions, yet suffer from critical optimizer inefficiencies; notably basis redundancy in LoRA's $B$ matrix when using AdamW, which fundamentally limits performance. We address this by optimizing the $B$ matrix on the Stiefel manifold, imposing explicit orthogonality constraints that achieve near-perfect orthogonality and ful…

Reciprocal Beyond-Diagonal Reconfigurable Intelligent Surface (BD-RIS): Scattering Matrix Design via Manifold Optimization
Marko Fidanovski, Iv\'an Alexander Morales Sandoval, Hyeon Seok Rou, Giuseppe Thadeu Freitas de Abreu, Emil Bj\"ornson
https://arxiv.org/abs/2509.20246

Reciprocal Beyond-Diagonal Reconfigurable Intelligent Surface (BD-RIS): Scattering Matrix Design via Manifold Optimization
Beyond-diagonal reconfigurable intelligent surfaces (BD-RISs) are emerging as a transformative technology in wireless communications, enabling enhanced performance and quality of service (QoS) of wireless systems in harsh urban environments due to their relatively low cost and advanced signal processing capabilities. Generally, BD-RIS systems are employed to improve robustness, increase achievable rates, and enhance energy efficiency of wireless systems in both direct and indirect ways. The dir…

Getting the manifold right: The crucial role of orbital resolution in DFT U for mixed d-f electron compounds
Kinga Warda, Eric Macke, Iurii Timrov, Lucio Colombi Ciacchi, Piotr M. Kowalski
https://arxiv.org/abs/2508.16435

Getting the manifold right: The crucial role of orbital resolution in DFT+U for mixed d-f electron compounds
Accurately modeling compounds with partially filled $d$ and $f$ shells remains a hard challenge for density-functional theory, due to large self-interaction errors stemming from local or semi-local exchange-correlation functionals. Hubbard $U$ corrections can mitigate such errors, but are often detrimental to the description of hybridized states, leading to spurious force contributions and wrong lattice structures. Here, we show that careful disentanglement of localized and delocalized states l…

Data-Driven Dynamic Factor Modeling via Manifold Learning
Graeme Baker, Agostino Capponi, J. Antonio Sidaoui
https://arxiv.org/abs/2506.19945 https://

Data-Driven Dynamic Factor Modeling via Manifold Learning
We propose a data-driven dynamic factor framework where a response variable depends on a high-dimensional set of covariates, without imposing any parametric model on the joint dynamics. Leveraging Anisotropic Diffusion Maps, a nonlinear manifold learning technique introduced by Singer and Coifman, our framework uncovers the joint dynamics of the covariates and responses in a purely data-driven way. We approximate the embedding dynamics using linear diffusions, and exploit Kalman filtering to pr…

Geometric Measures of Complexity for Open and Closed Quantum Systems
Alberto Acevedo, Antonio Falco
https://arxiv.org/abs/2507.18440 https://arxiv.org/pdf/…

Geometric Measures of Complexity for Open and Closed Quantum Systems
The unitary dynamics of quantum systems can be modeled as a trajectory on a Riemannian manifold. This theoretical framework naturally yields a purely geometric interpretation of computational complexity for quantum algorithms, a notion originally developed by Michael Nielsen (Circa, 2007). However, for nonunitary dynamics, it is unclear how one can recover a completely geometric characterization of Nielsen-like geometric complexity. The main obstacle to overcome is that nonunitary dynamics cann…

"The Meanings of a Publication in the Humanities: Meaning, text, and authorship in critical perspective" by
Marcel Knöchelmann: #publications

On semi-finite vector bundles with connection over Kahler manifolds
Sanjay Amrutiya, Indranil Biswas
https://arxiv.org/abs/2508.17048 https://arxiv.org/pdf…

On semi-finite vector bundles with connection over Kahler manifolds
Let $X$ be a compact connected Kähler manifold. We consider the category $\mathcal{C}^\mathrm{EC}(X)$ of flat holomorphic connections $(E,\, \nabla^E)$ over $X$ satisfying the condition that the underlying holomorphic vector bundle $E$ admits a filtration of holomorphic subbundles preserved by the connection $\nabla^E$ such that the monodromy of the induced connection on each successive quotient has finite image. The category $\mathcal{C}^\mathrm{EC}(X)$, equipped with the neutral fiber functo…

A unified multi-perspective quadratic manifold for mitigating the Kolmogorov barrier in multiphysics damage
Qinghua Zhang, Stephan Ritzert, Jian Zhang, Jannick Kehls, Stefanie Reese, Tim Brepols
https://arxiv.org/abs/2508.18220

A unified multi-perspective quadratic manifold for mitigating the Kolmogorov barrier in multiphysics damage
In multiphysics damage problems, material degradation is often modeled using local or global damage variables, whose evolution introduces strong nonlinearities and significant computational costs. Linear projection-based reduced-order models (ROMs) are widely used to accelerate these simulations but often fail to capture complex nonlinear damage evolution effectively. This limitation arises from the slow decay of the Kolmogorov n-width, which leads to a phenomenon known as the Kolmogorov barrie…

A Riemannian AdaGrad-Norm Method
Glaydston de C. Bento, Geovani N. Grapiglia, Mauricio S. Louzeiro, Daoping Zhang
https://arxiv.org/abs/2509.19682 https://…

A Riemannian AdaGrad-Norm Method
We propose a manifold AdaGrad-Norm method (\textsc{MAdaGrad}), which extends the norm version of AdaGrad (AdaGrad-Norm) to Riemannian optimization. In contrast to line-search schemes, which may require several exponential map computations per iteration, \textsc{MAdaGrad} requires only one. Assuming the objective function $f$ has Lipschitz continuous Riemannian gradient, we show that the method requires at most $\mathcal{O}(\varepsilon^{-2})$ iterations to compute a point $x$ such that $\|\…

Reversible Kalman Filter for state estimation with Manifold
Svyatoslav Covanov, Cedric Pradalier
https://arxiv.org/abs/2509.18224 https://arxiv.org/pdf/250…

Generative Model Inversion Through the Lens of the Manifold Hypothesis
Xiong Peng, Bo Han, Fengfei Yu, Tongliang Liu, Feng Liu, Mingyuan Zhou
https://arxiv.org/abs/2509.20177 ht…

Generative Model Inversion Through the Lens of the Manifold Hypothesis
Model inversion attacks (MIAs) aim to reconstruct class-representative samples from trained models. Recent generative MIAs utilize generative adversarial networks to learn image priors that guide the inversion process, yielding reconstructions with high visual quality and strong fidelity to the private training data. To explore the reason behind their effectiveness, we begin by examining the gradients of inversion loss with respect to synthetic inputs, and find that these gradients are surprisi…

On bifoliated planes, their structure and group actions
Mauro Camargo
https://arxiv.org/abs/2509.19961 https://arxiv.org/pdf/2509.19961

On bifoliated planes, their structure and group actions
Bifoliated planes arise naturally in the study of Anosov flows on $3$-manifolds. To any Anosov flow on a $3$-manifold $M$, one can associate a bifoliated plane equipped with an action of the fundamental group of $M$ which encodes the topology of the flow. This thesis begins by showing left-orderability of any group acting faithfully on a bifoliated plane. We then describe the bifoliated planes associated with two families of Anosov flows which are constructed from algebraic and combinatorial …

Lengths of Orthogonal Geodesic Chords on Riemannian Manifolds
Isabel Beach, Hayde\'e Contreras-Peruyero, Erin Griffin, Regina Rotman, Catherine Searle
https://arxiv.org/abs/2509.19620

Lengths of Orthogonal Geodesic Chords on Riemannian Manifolds
Let $N$ be a closed submanifold of a complete manifold, $M$. Then under certain topological conditions, there exists an orthogonal geodesic chord beginning and ending in $N$. In this paper we establish an upper bound for the length of such a geodesic chord in terms of geometric bounds on $M$. For example, if $N$ is a $2$-dimensional sphere embedded in a closed Riemannian $n$-manifold, then there exists an orthogonal geodesic chord in $M$ with endpoints on $N$ that has length at most $$ (4d+96D …

Left-handed geodesic flow of spheres of revolution
Pierre Dehornoy, Ana Rechtman
https://arxiv.org/abs/2506.19979 https://arxiv.org/p…

Left-handed geodesic flow of spheres of revolution
A flow on a 3-manifold is left-handed if any two ergodic invariant measures have negative linking number. We prove that on a 2-sphere of revolution whose curvature is $1/4$-pinched the geodesic flow is left-handed. Conversely, for every $δ\le 1/4$, we construct a 2-sphere whose curvature is $δ$-pinched and whose geodesic flow is not left-handed. This gives credit to a conjecture of Florio and Hryniewicz that $1/4$ is the optimal pinching constant for left-handedness among arbitrary positively…

Manifold Optics
Hongming Shen, Wen Xiao, Fei Fang Chuang, Huanyang Chen
https://arxiv.org/abs/2507.17437 https://arxiv.org/pdf/2507.17437

Manifold Optics
Transformation optics establishes an equivalence relationship between gradient media and curved space, unveiling intrinsic geometric properties of gradient media. However, this approach based on curved spaces is concentrated on two-dimensional manifolds, namely curved surfaces. In this Letter, we establish an intrinsic connection between three-dimensional manifolds and three-dimensional gradient media in transformation optics by leveraging the Yamabe problem and Ricci scalar curvature, a measur…

Quantum Gravity and Inflation as an Open System: A New Paradigm
Alan Sebasti\'an Morales, Mauricio Bellini, Juan Ignacio Musmarra
https://arxiv.org/abs/2509.19507 https://…

Quantum Gravity and Inflation as an Open System: A New Paradigm
As part of our program to develop a general theory of relativity for open systems, we introduce a covariant theory that incorporates the effects of classical and quantum spacetime alterations in a new metric tensor that effectively includes these alterations, thereby generating a Riemannian manifold from a new varied action without boundary terms. We illustrate the theory by studying an inflationary model which incorporates the quantum feedback effects of spacetime on the dynamics of the inflat…

A parametric tensor ROM for the shallow water dam break problem
Md Rezwan Bin Mizan, Maxim Olshanskii, Ilya Timofeyev
https://arxiv.org/abs/2506.20007 http…

A parametric tensor ROM for the shallow water dam break problem
We develop a variant of a tensor reduced-order model (tROM) for the parameterized shallow-water dam-break problem. This hyperbolic system presents multiple challenges for model reduction, including a slow decay of the Kolmogorov $N$-width of the solution manifold, shock formation, and the loss of smooth solution dependence on parameters. These issues limit the performance of traditional Proper Orthogonal Decomposition based ROMs. Our tROM approach, based on a low-rank tensor decomposition, buil…

Frobenius Algebras, Factorization Homology and the Reshetikhin-Turaev Invariants
Deniz Yeral
https://arxiv.org/abs/2508.16351 https://arxiv.org/pdf/2508.16…

Frobenius Algebras, Factorization Homology and the Reshetikhin-Turaev Invariants
For a ribbon fusion category $\mathcal{A}$ and a special symmetric commutative Frobenius algebra $F$ in $\mathcal{A}$, we use factorization homology and the ansular correlators obtained via the modular microcosm principle to construct a diffeomorphism invariant vector inside the skein module of any closed oriented three-dimensional manifold. If $\mathcal{A}$ is a modular fusion category and $F$ is the monoidal unit, this recovers the Reshetikhin-Turaev invariants.

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#FossilFuels #Climate #ClimateChange

Spin-polaron fingerprints in the optical conductivity of iridates
Francesco Cassol, L\'eo Gaspard, Cyril Martins, Michele Casula, Benjamin Lenz
https://arxiv.org/abs/2509.20337

Spin-polaron fingerprints in the optical conductivity of iridates
As a consequence of their spin-orbit entangled ground state, many $5d^{5}$ iridate materials display a peculiar double peak structure in optical transport quantities, such as absorption and conductivity. Their common interpretation is based on the presence of Hubbard subbands in the half-filled $j_{\mathrm{eff}}=1/2$ manifold. Herein, we challenge this picture, proposing a scenario based on the presence of spin-polaron (SP) quasiparticles, and assigning a dominant SP character to the first peak…

SOE: Sample-Efficient Robot Policy Self-Improvement via On-Manifold Exploration
Yang Jin, Jun Lv, Han Xue, Wendi Chen, Chuan Wen, Cewu Lu
https://arxiv.org/abs/2509.19292 https:…

Quantized and nonquantized Hall response in topological Hatsugai-Kohmoto systems
Thibaut Desort, Mark O. Goerbig, Corentin Morice
https://arxiv.org/abs/2506.20491

Quantized and nonquantized Hall response in topological Hatsugai-Kohmoto systems
We explore the robustness of Hall conductivity quantization in several insulating systems, exhibiting one scenario where the quantization is not preserved. Specifically, we apply the Kubo formula to topological models with the Hatsugai-Kohmoto interaction. Starting from the many-body degeneracy induced by this interaction in the topological Kane-Mele model, we consider Zeeman fields to select specific states within the ground-state manifold that reveal a non-quantized Hall response, precisely f…

Quantum Harmonic Analysis and the Structure in Data: Augmentation
Monika Doerfler, Franz Luef, Henry McNulty
https://arxiv.org/abs/2509.19474 https://arxiv…

Quantum Harmonic Analysis and the Structure in Data: Augmentation
In this short note, we study the impact of data augmentation on the smoothness of principal components of high-dimensional datasets. Using tools from quantum harmonic analysis, we show that eigenfunctions of operators corresponding to augmented data sets lie in the modulation space $M^1(\mathbb{R}^d)$, guaranteeing smoothness and continuity. Numerical examples on synthetic and audio data confirm the theoretical findings. While interesting in itself, the results suggest that manifold learning an…

Curved Kakeya sets for generic phases in odd dimensions
Shaoming Guo, Diankun Liu, Yakun Xi
https://arxiv.org/abs/2508.17706 https://arxiv.org/pdf/2508.177…

Curved Kakeya sets for generic phases in odd dimensions
We show that for each odd integer $n\ge 3$, there is an open dense subset of Hörmander phase functions in $\mathbb{R}^n$ for which the associated curved Kakeya sets have Hausdorff dimension at least $\frac{n+1}{2} + d_n$ for some positive $d_n$, thereby exceeding the classical compression threshold. In particular, in $\mathbb{R}^3$, generic Hörmander phases induce curved Kakeya sets of dimension at least $2 + \tfrac17$. As an application, on a generic three-dimensional Riemannian manifold, ev…

Quantum Optimal Control with Geodesic Pulse Engineering
Dylan Lewis, Roeland Wiersema, Sougato Bose
https://arxiv.org/abs/2508.16029 https://arxiv.org/pdf/…

Quantum Optimal Control with Geodesic Pulse Engineering
Designing multi-qubit quantum logic gates with experimental constraints is an important problem in quantum computing. Here, we develop a new quantum optimal control algorithm for finding unitary transformations with constraints on the Hamiltonian. The algorithm, geodesic pulse engineering (GEOPE), uses differential programming and geodesics on the Riemannian manifold of $\textrm{SU}(2^n)$ for $n$ qubits. We demonstrate significant improvements over the widely used gradient-based method, GRAPE, …

Invariants of stably trivial vector bundles with connection
Sergiu Moroianu
https://arxiv.org/abs/2509.21288 https://arxiv.org/pdf/2509.21288

Invariants of stably trivial vector bundles with connection
We define a Chern--Simons invariant of connections on stably trivial vector bundles over smooth manifolds, taking values in $3$-forms modulo closed forms with integral cohomology class. We show an additivity property of this invariant for connections defined on a direct sum of bundles, under a certain block-diagonality condition on the curvature. As a corollary, we deduce an obstruction for conformally immersing a $n$-dimensional Riemannian manifold in a translation manifold of dimension $n+1$.

Orthonormal Strichartz estimates on torus and waveguide manifold and applications
Divyang G. Bhimani, Subhash. R. Choudhary
https://arxiv.org/abs/2507.16712

Orthonormal Strichartz estimates on torus and waveguide manifold and applications
We establish orthonormal Strichartz estimates for the fractional Schrödinger equations on torus and waveguide manifold. In the process, we also improve $\ell^2$ decoupling inequality and establish classical fractional Strichartz estimates on waveguide manifold. This maybe of independent interest. As an application, we establish local well-posednes for the Hartree equations with infinitely many particles with non-trace class initial data.

MA-DPR: Manifold-aware Distance Metrics for Dense Passage Retrieval
Yifan Liu, Qianfeng Wen, Mark Zhao, Jiazhou Liang, Scott Sanner
https://arxiv.org/abs/2509.13562 https://

MA-DPR: Manifold-aware Distance Metrics for Dense Passage Retrieval
Dense Passage Retrieval (DPR) typically relies on Euclidean or cosine distance to measure query-passage relevance in embedding space, which is effective when embeddings lie on a linear manifold. However, our experiments across DPR benchmarks suggest that embeddings often lie on lower-dimensional, non-linear manifolds, especially in out-of-distribution (OOD) settings, where cosine and Euclidean distance fail to capture semantic similarity. To address this limitation, we propose a manifold-aware …

A generalized canonical metric for optimization on the indefinite Stiefel manifold
Dinh Van Tiep, Duong Thi Viet An, Nguyen Thi Ngoc Oanh, Nguyen Thanh Son
https://arxiv.org/abs/2509.16113

A generalized canonical metric for optimization on the indefinite Stiefel manifold
Various tasks in scientific computing can be modeled as an optimization problem on the indefinite Stiefel manifold. We address this using the Riemannian approach, which basically consists of equipping the feasible set with a Riemannian metric, preparing geometric tools such as orthogonal projections, formulae for Riemannian gradient, retraction and then extending an unconstrained optimization algorithm on the Euclidean space to the established manifold. The choice for the metric undoubtedly has…

Localization of strings on group manifolds
Sameer Murthy, Edward Witten
https://arxiv.org/abs/2506.20028 https://arxiv.org/pdf/2506.2…

Localization of strings on group manifolds
We compute the partition function of the WZW model with target a compact Lie group $G$ by adapting a method used by Choi and Takhtajan to compute the heat kernel of the group manifold. The basic idea is to compute the partition function of a supersymmetric version of the WZW model using a form of supersymmetric localization and then use the fact that, since the fermions of the supersymmetric WZW model are actually decoupled from the bosons, this also determines the partition function of the pur…

Improving Cram\'er-Rao Bound And Its Variants: An Extrinsic Geometry Perspective
Sunder Ram Krishnan
https://arxiv.org/abs/2509.17886 https://arxiv.org…

Improving Cramér-Rao Bound And Its Variants: An Extrinsic Geometry Perspective
This work presents a geometric refinement of the classical Cramér-Rao bound (CRB) by incorporating curvature-aware corrections based on the second fundamental form associated with the statistical model manifold. That is, our formulation shows that relying on the extrinsic geometry of the square root embedding of the manifold in the ambient Hilbert space comprising square integrable functions with respect to a fixed base measure offers a rigorous (and intuitive) way to improve upon the CRB and …

Random coverage of a manifold with boundary
Mathew D. Penrose, Xiaochuan Yang
https://arxiv.org/abs/2509.19278 https://arxiv.org/pdf/2509.19278

Pre-Lagrangian tori transverse to an Anosov flow
Francesco Ruscelli
https://arxiv.org/abs/2508.17396 https://arxiv.org/pdf/2508.17396

Pre-Lagrangian tori transverse to an Anosov flow
An Anosov flow on a smooth three-manifold \( M \) gives rise to a Liouville structure on \( \mathbb{R} \times M \) by a construction of Mitsumatsu. In a recent paper, Cieliebak, Lazarev, Massoni and Moreno ask whether an embedded torus \( Σ\subseteq M \) transverse to an Anosov flow gives rise to a Lagrangian in \( \mathbb{R} \times M \). We show that the answer to this question is in general negative by finding a topological obstruction related to the foliations induced on the torus by the we…

A Consensus Algorithm for Second-Order Systems Evolving on Lie Groups
Akhil B Krishna, Farshad Khorrami, Anthony Tzes
https://arxiv.org/abs/2508.17473 https://

A Consensus Algorithm for Second-Order Systems Evolving on Lie Groups
In this paper, a consensus algorithm is proposed for interacting multi-agents, which can be modeled as simple Mechanical Control Systems (MCS) evolving on a general Lie group. The standard Laplacian flow consensus algorithm for double integrator systems evolving on Euclidean spaces is extended to a general Lie group. A tracking error function is defined on a general smooth manifold for measuring the error between the configurations of two interacting agents. The stability of the desired consens…

GhostUMAP2: Measuring and Analyzing (r,d)-Stability of UMAP
Myeongwon Jung, Takanori Fujiwara, Jaemin Jo
https://arxiv.org/abs/2507.17174 https://

GhostUMAP2: Measuring and Analyzing (r,d)-Stability of UMAP
Despite the widespread use of Uniform Manifold Approximation and Projection (UMAP), the impact of its stochastic optimization process on the results remains underexplored. We observed that it often produces unstable results where the projections of data points are determined mostly by chance rather than reflecting neighboring structures. To address this limitation, we introduce (r,d)-stability to UMAP: a framework that analyzes the stochastic positioning of data points in the projection space. …

Performance of High-Intensity Electron Linacs as Drivers for Compact Neutron Sources
Javier Olivares Herrador, Laurence M. Wroe, Andrea Latina, Roberto Corsini, Walter Wuensch, Steinar Stapnes, Nuria Fuster-Mart{\i}nez, Benito Gimeno, Daniel Esperante
https://arxiv.org/abs/2506.20313

Performance of High-Intensity Electron Linacs as Drivers for Compact Neutron Sources
The demand for neutron production facilities is increasing, as the applications of neutron science are manifold. These applications drive the need for efficient and compact neutron sources. In this context, this paper explores the potential performance of normal-conducting compact electron linacs from 20 MeV to 500 MeV as drivers for neutron sources. Results from a G4BEAMLINE simulation study find optimum dimensions of a tungsten target and characterize the emitted neutron spectrum. Two electro…

Stochastic perturbation of geodesics on the manifold of Riemannian metrics
Ana Bela Cruzeiro, Ali Suri
https://arxiv.org/abs/2507.16959 https://arxiv.org/p…

Stochastic perturbation of geodesics on the manifold of Riemannian metrics
In this paper, using diffusion processes, we compute the evolution equation on the manifold of Riemannian metrics for the Lagrangian induced by the $L^2$ stochastic kinetic energy functional.

QFT on rotating boxes at finite temperature
Sebestyen Nagy, Daniel Nogradi
https://arxiv.org/abs/2509.19933 https://arxiv.org/pdf/2509.19933

QFT on rotating boxes at finite temperature
We formulate thermal quantum field theory on a finite spatial periodic volume undergoing rotation. Traditional compactifications at finite temperature without rotations typically involve ${\mathbb T}^4$ as the space-time manifold within a path integral formulation and also moving frames can be accommodated by shifted boundary conditions on the same space. We show that consistent descriptions of a rotating box are possible on space-time manifolds with topology different from ${\mathbb T}^4$ but …

Packing stability and the subleading asymptotics of symplectic Weyl laws
Oliver Edtmair
https://arxiv.org/abs/2509.15390 https://arxiv.org/pdf/2509.15390…

Packing stability and the subleading asymptotics of symplectic Weyl laws
We prove that symplectic ball packing stability holds for every compact, connected symplectic $4$-manifold with smooth boundary. This follows from a stronger result: the full volume of any such manifold can be filled by a single symplectic ellipsoid. As an application, we obtain estimates - with sharp exponents - for the error terms in the symplectic Weyl laws for embedded contact homology capacities, periodic Floer homology spectral invariants, and link spectral invariants. We also construct a…

Revealing Neurocognitive and Behavioral Patterns by Unsupervised Manifold Learning from Dynamic Brain Data
Zixia Zhou, Junyan Liu, Wei Emma Wu, Ruogu Fang, Sheng Liu, Qingyue Wei, Rui Yan, Yi Guo, Qian Tao, Yuanyuan Wang, Md Tauhidul Islam, Lei Xing
https://arxiv.org/abs/2508.11672

Revealing Neurocognitive and Behavioral Patterns by Unsupervised Manifold Learning from Dynamic Brain Data
Dynamic brain data, teeming with biological and functional insights, are becoming increasingly accessible through advanced measurements, providing a gateway to understanding the inner workings of the brain in living subjects. However, the vast size and intricate complexity of the data also pose a daunting challenge in reliably extracting meaningful information across various data sources. This paper introduces a generalizable unsupervised deep manifold learning for exploration of neurocognitive…

Alternative tangent and cotangent structures and their physical applications
Jos\'e F. Cari\~nena, Jes\'us Clemente-Gallardo, Giuseppe Marmo
https://arxiv.org/abs/2509.20855

Alternative tangent and cotangent structures and their physical applications
The conditions under which a given manifold $M$ may be given a tangent bundle or a cotangent bundle structure are analyzed. This is an important property arising in different contexts. For instance, in the study of integrability of a given dynamics the existence of alternative compatible structures is very relevant, as well as in the geometric approach to Classical Mechanics. On the other hand in the quantum-to-classical transition, a Weyl system plays an important role for it provides (within …

This is the manifold typt thing that I am currently roughing together for the 2nd pump from the main pond.
The through pipe will go to the filter and the two offshoots will go to the bottom returns and side sorayers which are both meant to keep the water in the pond moving toward the pump bay and discourage settling on the bottom
#poolpond #diy #backyardproject

Regularity of Resolutions and Limits of Manifolds with a Uniform Contractibility Function
Mohammad Alattar, Lewis Tadman
https://arxiv.org/abs/2507.17557 https://

Regularity of Resolutions and Limits of Manifolds with a Uniform Contractibility Function
In this paper, we give a short and self-contained proof to a 1991 conjecture by Moore concerning the structure of certain finite-dimensional Gromov--Hausdorff limits, in the ANR setting. As a consequence, one easily characterizes finite dimensional limits of PL-able or Riemannian $n$-manifolds with a uniform contractibility function. For example, one can define for any compact connected metric space that is a resolvable ANR homology manifold of covering dimension at least 5, an obstruction, whi…

Homogenization and 3D-2D dimension reduction of a functional on manifold valued Sobolev spaces
Michela Eleuteri, Luca Lussardi, Andrea Torricelli, Elvira Zappale
https://arxiv.org/abs/2507.16386

Homogenization and 3D-2D dimension reduction of a functional on manifold valued Sobolev spaces
We study simultaneous homogenization and dimensional reduction of integral functionals for maps in manifold-valued Sobolev spaces. Due to the superlinear growth regime, we prove that the density of the $Γ$-limit is a tangential quasiconvex integrand represented by a cell formula.

Geodesic Tracing-Based Kinematic Integration of Rolling and Sliding Contact on Manifold Meshes for Dexterous In-Hand Manipulation
Sunyu Wang, Arjun S. Lakshmipathy, Jean Oh, Nancy S. Pollard
https://arxiv.org/abs/2508.12439

Geodesic Tracing-Based Kinematic Integration of Rolling and Sliding Contact on Manifold Meshes for Dexterous In-Hand Manipulation
Reasoning about rolling and sliding contact, or roll-slide contact for short, is critical for dexterous manipulation tasks that involve intricate geometries. But existing works on roll-slide contact mostly focus on continuous shapes with differentiable parametrizations. This work extends roll-slide contact modeling to manifold meshes. Specifically, we present an integration scheme based on geodesic tracing to first-order time-integrate roll-slide contact directly on meshes, enabling dexterous m…

Lipschitz Continuity and Formulas of the Gradient Vector of the SRB Entropy Functional
Jianyu Chen, Miaohua Jiang
https://arxiv.org/abs/2509.18596 https://…

Smoothing topological pseudo-isotopies of 4-manifolds
Patrick Orson, Mark Powell, Oscar Randal-Williams
https://arxiv.org/abs/2507.16984 https://arxiv.org/…

Smoothing topological pseudo-isotopies of 4-manifolds
Given a closed, smooth 4-manifold $X$ and self-diffeomorphism $f$ that is topologically pseudo-isotopic to the identity, we study the question of whether $f$ is moreover smoothly pseudo-isotopic to the identity. If the fundamental group of $X$ lies in a certain class, which includes trivial, free, and finite groups of odd order, we show the answer is always affirmative. On the other hand, we produce the first examples of manifolds $X$ and diffeomorphisms $f$ where the answer is negative. Our in…

On solutions to Hardy-Sobolev equations on Riemannian manifolds
Guillermo Henry, Jimmy Petean
https://arxiv.org/abs/2506.20089 https://

On solutions to Hardy-Sobolev equations on Riemannian manifolds
Let $(M,g)$ be a closed Riemannian manifold of dimension at least $3$. Let $S$ be the union of the focal submanifolds of an isoparametric function on $(M,g)$. In this article we address the existence of solutions of the Hardy-Sobolev type equation $Δ_g u+K(x)u=\frac{u^{q-1}}{\left(d_{S}(x)\right)^s}$, where $d_{S}(x)$ is the distance from $x$ to $S$ and $q>2$. In particular, we will prove the existence of infinite sign-changing solutions to the equation.

On the problem of filling by a Poincar\'e-Einstein metric in dimension 4
Sun-Yung Alice Chang, Yuxin Ge
https://arxiv.org/abs/2509.18430 https://arxiv.…

Recovering Wasserstein Distance Matrices from Few Measurements
Muhammad Rana, Abiy Tasissa, HanQin Cai, Yakov Gavriyelov, Keaton Hamm
https://arxiv.org/abs/2509.19250 https://…

Recovering Wasserstein Distance Matrices from Few Measurements
This paper proposes two algorithms for estimating square Wasserstein distance matrices from a small number of entries. These matrices are used to compute manifold learning embeddings like multidimensional scaling (MDS) or Isomap, but contrary to Euclidean distance matrices, are extremely costly to compute. We analyze matrix completion from upper triangular samples and Nyström completion in which $\mathcal{O}(d\log(d))$ columns of the distance matrices are computed where $d$ is the desired embe…

O(4,4) dualities and Manin triples
Angelina Kurenkova, Edvard T. Musaev
https://arxiv.org/abs/2509.19144 https://arxiv.org/pdf/2509.19144

Mapping Microstructure: Manifold Construction for Accelerated Materials Exploration
Simon A. Mason, Megna N. Shah, Jeffrey P. Simmons, Dennis M. Dimiduk, Stephen R. Niezgoda
https://arxiv.org/abs/2509.15022

Mapping Microstructure: Manifold Construction for Accelerated Materials Exploration
Accelerating materials development requires quantitative linkages between processing, microstructure, and properties. In this work, we introduce a framework for mapping microstructure onto a low-dimensional material manifold that is parametrized by processing conditions. A key innovation is treating microstructure as a stochastic process, defined as a distribution of microstructural instances rather than a single image, enabling the extraction of material state descriptors that capture the esse…

Quantum Beatings in Optical Cavities
Ishaan Ganti, Jianshu Cao
https://arxiv.org/abs/2507.17339 https://arxiv.org/pdf/2507.17339

Quantum Beatings in Optical Cavities
Cavity polaritons, quasiparticles formed by coherent light-matter coupling, are at the heart of fundamental concepts of quantum optics. The quintessential signature of this coherent coupling is the Rabi oscillation, which results from the neglect of the counter-rotating-wave (CRW) effect in the weak-coupling regime. The goal of this letter is to predict resonant beatings that envelop the Rabi oscillation on the second or higher excitation manifold. These polariton beatings arise from the CRW te…

Hypercomplex analytic spaces and schemes
Roger Bielawski
https://arxiv.org/abs/2507.16452 https://arxiv.org/pdf/2507.16452

Hypercomplex analytic spaces and schemes
We propose definitions of hypercomplex analytic spaces and hypercomplex schemes. We show that such a hypercomplex space is canonically associated to the quotient of a hypercomplex manifold by a finite group action.

Vector field cycles in the tangent bundle
Santiago R. Simanca
https://arxiv.org/abs/2508.17441 https://arxiv.org/pdf/2508.17441

Vector field cycles in the tangent bundle
Given a closed Riemannian manifold $(M^m,g)$ and a vector field $v$ on $M$, we form the Sasaki metric $g_S$ on $TM$, and restrict it to the image of the cross section map of $M$ into $TM$ defined by $v$, whose pull back to $M$ defines a new metric $g(v)$ on $M$. We then view the cross section as an isometric embedding $f_{g(v)}: (M,g(v))\rightarrow (TM,g_S)$, which when $\| v\|_g=1$, ranges into the unit sphere bundle $(S^1(TM),g_S)$. $v$ is minimal or minimal unit if these embeddings…

Classification of locally standard torus actions
Yael Karshon, Shintaro Kuroki
https://arxiv.org/abs/2507.15004 https://arxiv.org/pdf/2507.15004

Classification of locally standard torus actions
An action of a torus T on a manifold M is locally standard if, at each point, the stabilizer is a sub-torus and the non-zero isotropy weights are a basis to its weight lattice. The quotient M/T is then a manifold-with-corners, decorated by a so-called unimodular labelling, which keeps track of the isotropy representations in M, and by a degree two cohomology class with coefficients in the integral lattice of the Lie algebra of T, which encodes the "twistedness" of M over M/T. We classify locall…

Hot spots on cones and warped product manifolds
Lawford Hatcher
https://arxiv.org/abs/2508.18054 https://arxiv.org/pdf/2508.18054

Hot spots on cones and warped product manifolds
We study extrema of solutions to the heat equation (i.e. hot spots) on certain types of warped product manifolds of the form $([0,L]\times M,dr^2+f(r)^2h)$ where $(M,h)$ is a closed Riemannian manifold. We prove that, under certain conditions on the warping function $f$, the statement of Rauch's hot spots conjecture holds for the corresponding warped product. We then go on to study the long-time behavior of hot spots on infinite cones over closed Riemannian manifolds. In this case, under approp…

A Complete Derivation of Complex Circle Manifold (CCM) Riemannian manifold Optimization Equations
Amirreza Tabrizi, Mohammad Hadi Mirmohammadi
https://arxiv.org/abs/2508.07396 h…

A Complete Derivation of Complex Circle Manifold (CCM) Riemannian manifold Optimization Equations
After reviewing manifold optimization techniques in applications like MIMO communication systems, phased array beamforming, radar, and control theory, we observed that the Complex Circle Manifold (CCM) is widely employed, yet its foundational relations and equations lack a rigorous, self-contained derivation in the literature. This paper provides a systematic and rigorous proof of CCM's key properties, including its tangent space and Riemannian gradient operations, with explicit connections to …

The matched projection and geodesics of the Grassmann manifold
Esteban Andruchow
https://arxiv.org/abs/2508.14870 https://arxiv.org/pdf/2508.14870

The matched projection and geodesics of the Grassmann manifold
Given an idempotent operator $E$ in a complex Hilbert space ${\mathcal H}$, one can associate to it two orthogonal projections: - The polar decomposition $2E-1=(2P-1)|2E-1|$ provides an orthogonal projection $P$. That the unitary part in the decomposition of $2E-1$ is of this form, i.e., a selfadjoint unitary operator, is a remarkable observation done by G. Corach, H. Porta and L. Recht (see references below). - The question of which, among all orthogonal projections, is the one c…

Reduction principles for proper actions
Leonardo Biliotti, Gustavo May Custodio, Alessandro Minuzzo
https://arxiv.org/abs/2509.19915 https://arxiv.org/pdf/…

Reduction principles for proper actions
We study the core of a proper action by a Lie group $G$ on a smooth manifold $M$, extending the construction for $G$ compact by Skjelbred and Straume. Moreover, we show that many properties of a proper $G$-action on $M$ are determined by the action of a group $G'$ on the corresponding core $_cM$. We say that such properties admit a reduction principle. In particular, we prove that a proper isometric $G$-action on $M$ is polar (resp. hyperpolar) if and only if the $G'$-action on $_cM$ is polar (…

Non-Lagrangian phases of matter from Wilsonian renormalization of 3D Wess-Zumino-Witten theory on Stiefel manifolds
Shouryya Ray
https://arxiv.org/abs/2509.18966 https://…

Non-Lagrangian phases of matter from Wilsonian renormalization of 3D Wess-Zumino-Witten theory on Stiefel manifolds
I study the renormalization of D-dimensional level-k Wess-Zumino-Witten theory with Stiefel-manifold target space $\mathrm{St}_{N,N-D-1} \cong \mathrm{SO}(N)/\mathrm{SO}(D+1)$, with a particular focus on $D = 3$. I investigate in particular whether such a theory admits IR-stable fixed points of the renormalization group flow. Such fixed points have been suggested to describe conformal phases of matter that do not have a known dual (super-)renormalizable Lagrangian for $N \geq 7$ in $D = 3$. The…

Levy Laplacian on manifold and heat flows of differential forms
Boris Volkov
https://arxiv.org/abs/2507.13013 https://arxiv.org/pdf/2…

Levy Laplacian on manifold and heat flows of differential forms
The Levy Laplacian is an infinite-dimensional differential operator, which is interesting for its connection with the Yang-Mills gauge fields. The article proves the equivalence of various definitions of the Levy Laplacian on the manifold of $H^1$-paths on a Riemannian manifold. The heat equation with the Levy Laplacian is considered. The tendency of some solutions of this heat equation to the locally constant functionals as time tends to infinity is studied. These solutions are constructed usi…

Robust Multi-Manifold Clustering via Simplex Paths
Haoyu Chen, Anna Little, Akin Narayan
https://arxiv.org/abs/2507.10710 https://arx…

Robust Multi-Manifold Clustering via Simplex Paths
This article introduces a novel, geometric approach for multi-manifold clustering (MMC), i.e. for clustering a collection of potentially intersecting, d-dimensional manifolds into the individual manifold components. We first compute a locality graph on d-simplices, using the dihedral angle in between adjacent simplices as the graph weights, and then compute infinity path distances in this simplex graph. This procedure gives a metric on simplices which we refer to as the largest angle path dista…

A Note on Non-Hydrodynamic Solutions of Kinetic Systems
Florian Kogelbauer, Ilya Karlin
https://arxiv.org/abs/2508.17370 https://arxiv.org/pdf/2508.17370…

A Note on Non-Hydrodynamic Solutions of Kinetic Systems
We show that the one-dimensional three-component Grad system admits solutions that violate the Chapman--Enskog scaling in Knudsen number. In particular, there exist solutions that do not converge to the analogues of the Euler and Navier--Stokes equations for vanishing Knudsen number. These non-hydrodynamic solutions correspond to a fast spectral manifold in kinetic phase space.

Integral points and volume of integral-integral affine manifolds
Oded Elisha, Yael Karshon, Yiannis Loizides
https://arxiv.org/abs/2508.17551 https://arxiv…

Integral points and volume of integral-integral affine manifolds
We give an elementary proof that, for a closed manifold with an integral-integral affine structure, its total volume and number of integral points coincide. This theorem was previously shown to be equivalent to the "independence of polarization" phenomenon of geometric quantization. The proof uses rational Ehrhart theory and elementary Fourier analysis to estimate the difference between the total volume and the number of integral points.

A positive mass theorem for non-smooth metrics on asymptotically flat manifolds with non-compact boundary
Sergio Almaraz, Shaodong Wang
https://arxiv.org/abs/2506.20453

A positive mass theorem for non-smooth metrics on asymptotically flat manifolds with non-compact boundary
On a smooth asymptotically flat Riemannian manifold with non-compact boundary, we prove a positive mass theorem for metrics which are only continuous across a compact hypersurface. As an application, we obtain a positive mass theorem on manifolds with non-compact corners.

Spike layered solutions for elliptic systems on Riemannian Manifolds
Anusree R Kannoth, Bhakti Bhusan Manna
https://arxiv.org/abs/2506.20300 https://

Spike layered solutions for elliptic systems on Riemannian Manifolds
In this article, we study the following Hamiltonian system: \begin{equation*} \begin{cases} \begin{aligned} &-\varepsilon^{2}Δ_{g} u +u = |v|^{q-1}v, &-\varepsilon^{2}Δ_{g} v +v = |u|^{p-1}u && \text{ in } \mathcal{M}, & \quad u,v >0 && \text{ in } \mathcal{M}, \end{aligned} \end{cases} \end{equation*} where $\mathcal{M}$ is a smooth, compact and connected Riemannian manifold of dimension $N\geq 3$ without boundary. The exponents $p,q>1$ are assumed to lie be…

Breaking the permutation character of diffeomorphisms on spinor structures
J. M. Hoff da Silva
https://arxiv.org/abs/2507.17737 https://arxiv.org/pdf/2507.…

Breaking the permutation character of diffeomorphisms on spinor structures
We investigate the impact of diffeomorphisms where more than one nonequivalent spinor structure is built upon a given base manifold endowed with nontrivial topology. We call attention to the fact that a relatively straightforward construction evinces a lack of symmetry between fermionic modes from different spinor bundle sections, leading to a dynamic preference breaking the permutation character of diffeomorphisms on spinor structures.

Do Riemannian Submersions Preserve Positive Intermediate Ricci Curvature?
Hasan M. El-Hasan, Russell Phelan, Frederick Wilhelm
https://arxiv.org/abs/2507.17839 https://

Do Riemannian Submersions Preserve Positive Intermediate Ricci Curvature?
Pro and the third author showed that there are Riemannian submersions $π: M \to B$ with $M$ a compact manifold with positive Ricci curvature, whose base $B$, has Ricci curvatures with both signs. Thus, Riemannian submersions need not preserve positive Ricci curvature. In this note we establish the degree to which this result extends into the setting of positive intermediate Ricci curvature. It is an immediate consequence of the Gray--O'Neill Horizontal curvature equation that if $π: M\to B$…

Detection of long-range coherence in driven hot atomic vapors by spin noise spectroscopy
Rupak Bag, Sayari Majumder, Saptarishi Chaudhuri, Dibyendu Roy
https://arxiv.org/abs/2509.18036

Detection of long-range coherence in driven hot atomic vapors by spin noise spectroscopy
We study intriguing dynamical features of hot Rubidium atoms driven by two light fields. The fields resonantly drive multiple Zeeman states within two hyperfine levels, yielding a cascaded-$Λ$ like structure in the frequency space. A non-Hermitian Floquet tight-binding lattice with imaginary hopping between the nearest states effectively describes the coherence dynamics between Zeeman states within the ground hyperfine manifold. By performing spin noise spectroscopy, we observe higher harmonic…

Frobenius manifold for the nodal quiver
Atsuki Nakago, Yuuki Shiraishi, Atsushi Takahashi
https://arxiv.org/abs/2509.12722 https://arxiv.org/pdf/2509.12722…

Frobenius manifold for the nodal quiver
Starting from the Weierstrass elliptic function, we study the associated Frobenius structure, incorporating the perspective of derived categories, particularly that of homological mirror symmetry. Given a deformation of the Weierstrass elliptic function, we construct a primitive form normalized to be compatible with the period map for integral cycles, and obtain a Frobenius structure whose Frobenius potential is defined over the rational numbers. We also construct a Frobenius structure using el…

On the space of metrics with non-positive curvature
Yasha Savelyev
https://arxiv.org/abs/2506.19983 https://arxiv.org/pdf/2506.19983

On the space of metrics with non-positive curvature
Let $\mathcal{M} (X)$ denote the space of complete Riemannian metrics with non-positive sectional curvature and with negatively curved ends, on a manifold $X$. We show that $\mathcal{M} (\mathbb{R} \times S ^{1}) $ and $\mathcal{M} (\mathbb{R} ^{} \times Y)$ are path disconnected, where $Y$ is compact and admits a negative curvature metric. The proof is very concise, using as the main ingredient Fuller index theory. Furthermore, we get a new metric deformation invariant based on geodesic string…

The Intrinsic Riemannian Proximal Gradient Method for Convex Optimization
Ronny Bergmann, Hajg Jasa, Paula John, Max Pfeffer
https://arxiv.org/abs/2507.16055

The Intrinsic Riemannian Proximal Gradient Method for Convex Optimization
We consider a class of (possibly strongly) geodesically convex optimization problems on Hadamard manifolds, where the objective function splits into the sum of a smooth and a possibly nonsmooth function. We introduce an intrinsic convex Riemannian proximal gradient (CRPG) method that employs the manifold proximal map for the nonsmooth step, without operating in the embedding or tangent space. A sublinear convergence rate for convex problems and a linear convergence rate for strongly convex prob…

Geometric, topological and dynamical properties of conformally symplectic systems, normally hyperbolic invariant manifolds, and scattering maps
Marian Gidea, Rafael de la Llave, Tere M-Seara
https://arxiv.org/abs/2508.14794

Geometric, topological and dynamical properties of conformally symplectic systems, normally hyperbolic invariant manifolds, and scattering maps
Conformally symplectic diffeomorphisms $f:M \rightarrow M$ transform a symplectic form $ω$ on a manifold $M$ into a multiple of itself, $f^* ω= ηω$. We assume $ω$ is bounded, as some of the results may fail otherwise. We show that there are deep interactions between the topological properties of the manifold, the dynamical properties of the map, and the geometry of invariant manifolds. We show that, when the symplectic form is not exact, the possible conformal factors $η$ are related …

Fr\'echet Geodesic Boosting
Yidong Zhou, Su I Iao, Hans-Georg M\"uller
https://arxiv.org/abs/2509.18013 https://arxiv.org/pdf/2509.18013

Fréchet Geodesic Boosting
Gradient boosting has become a cornerstone of machine learning, enabling base learners such as decision trees to achieve exceptional predictive performance. While existing algorithms primarily handle scalar or Euclidean outputs, increasingly prevalent complex-structured data, such as distributions, networks, and manifold-valued outputs, present challenges for traditional methods. Such non-Euclidean data lack algebraic structures such as addition, subtraction, or scalar multiplication required b…

On Weyl structures reducible in the direction of the Lee form
Jos\'e Luis Carmona Jim\'enez
https://arxiv.org/abs/2507.17496 https://arxiv.org/pdf/…

On Weyl structures reducible in the direction of the Lee form
A Weyl structure on a Riemannian manifold $(M,g)$ is a torsion-free linear connection $\nabla$ such that there is a $1$-form $θ$ (called the Lee form) satisfying $\nabla g = 2\, θ\otimes g$. We examine the case in which there exists a $\nabla$-parallel distribution of codimension $1$ on which the Lee form vanishes identically. We prove that if $(M,g)$ is complete with $θ$ closed, then the Weyl structure must be flat or exact. We apply this to show that every homogeneous Kenmotsu manifold is …

Stokes' theorem as an entropy-extremizing duality
Daniel Lazarev
https://arxiv.org/abs/2509.16386 https://arxiv.org/pdf/2509.16386

Stokes' theorem as an entropy-extremizing duality
Given a manifold $\mathcal{M} \subset \mathbb{R}^n$, we consider all subsets of $\mathcal{M}$ that satisfy the generalized Stokes' theorem and show that $\partial\mathcal{M}$ maximizes the associated information theoretic entropy functional. This provides an information theoretic characterization of the duality expressed by Stokes' theorem, whereby the boundary of a manifold is the `least informative' subset of the manifold satisfying the Stokes relation.

Homotopy classification of $4$-manifolds with $3$-manifold fundamental group
Jonathan Hillman, Daniel Kasprowski, Mark Powell, Arunima Ray
https://arxiv.org/abs/2508.07504 https…

Homotopy classification of $4$-manifolds with $3$-manifold fundamental group
We give a criterion on a group $π$ and a homomorphism $w \colon π\to C_2$ under which closed $4$-manifolds with fundamental group $π$ and orientation character $w$ are classified up to homotopy equivalence by their quadratic $2$-types. We verify the criterion for a large class of $3$-manifold groups and orientation characters, in particular for the fundamental group $π$ of any closed, orientable $3$-manifold whose finite subgroups are cyclic, provided $w$ vanishes on every element of $π$ o…

Einstein metrics, their moduli spaces and stability
Paul Schwahn, Uwe Semmelmann
https://arxiv.org/abs/2507.18463 https://arxiv.org/pdf/2507.18463

Einstein metrics, their moduli spaces and stability
This survey deals with two closely connected topics: first, the stability of Einstein metrics under the Einstein-Hilbert functional, and second, their deformation theory and the study of the moduli space of Einstein metrics on a compact manifold. To first order, both problems reduce to studying the spectrum and eigentensors of the Lichnerowicz Laplacian. We give an introduction to the classical theory and survey recent results and advances.

H\"older stability of an inverse spectral problem for the magnetic Schr\"odinger operator on a simple manifold
Boya Liu, Hadrian Quan, Teemu Saksala, Lili Yan
https://arxiv.org/abs/2507.13619

Hölder stability of an inverse spectral problem for the magnetic Schrödinger operator on a simple manifold
We show that on a simple Riemannian manifold, the electric potential and the solenoidal part of the magnetic potential appearing in the magnetic Schrödinger operator can be recovered Hölder stably from the boundary spectral data. This data contains the eigenvalues and the Neumann traces of the corresponding sequence of Dirichlet eigenfunctions of the operator. Our proof contains two parts, which we present in the reverse order. (1) We show that the boundary spectral data can be stably obtaine…

Weak Nearly $\mathcal S$- and Weak Nearly $\mathcal C$- Manifolds
Vladimir Rovenski
https://arxiv.org/abs/2508.17755 https://arxiv.org/pdf/2508.17755

Weak Nearly $\mathcal S$- and Weak Nearly $\mathcal C$- Manifolds
The recent interest of geometers in the $f$-structures of K. Yano (1961) is motivated by the study of the dynamics of contact foliations, as well as their applications in theoretical physics. Weak metric $f$-structures on a smooth manifold, introduced by of the author and R. Wolak (2022), open a new perspective on the theory of classical structures. In the paper, we define structures of this kind, called weak nearly ${\cal S}$- and weak nearly ${\cal C}$- structures, study their geometry, e.g. …

A Hyperbolic Inverse Problem for lower order terms on a closed manifold with disjoint data
Matti Lassas, Boya Liu, Teemu Saksala, Andrew Shedlock, Ziyao Zhao
https://arxiv.org/abs/2509.19008

Non-negative curvature on certain product manifolds
Wen Shen
https://arxiv.org/abs/2508.15194 https://arxiv.org/pdf/2508.15194

Non-negative curvature on certain product manifolds
Let $G/H$ be a closed, simply connected homogeneous manifold. Suppose every stable class of real vector bundles over $G/H$ contains a homogeneous bundle. Then, for any closed, simply connected smooth manifold $M$ homotopy equivalent to $G/H$, there exists $n>\mathrm{dim}(M)$ such that the product manifold $M\times S^{n}$ admits a metric with non-negative sectional curvature. Many homogeneous manifolds satisfy this assumption, including simply connected compact rank-one symmetric spaces, and amo…

The intersection of two real flag manifolds in a complex flag manifold
Osamu Ikawa, Hiroshi Iriyeh, Takayuki Okuda, Takashi Sakai, Hiroyuki Tasaki
https://arxiv.org/abs/2507.12785

The intersection of two real flag manifolds in a complex flag manifold
We give a necessary and sufficient condition for two real flag manifolds, which are not necessarily congruent, in a complex flag manifold to intersect transversally in terms of the symmetric triad. Then we show that the intersection of two real flag manifolds is antipodal. As an application, we prove that any real flag manifold in a complex flag manifold is a globally tight Lagrangian submanifold.

The second variational formula of the variational problems for mappings between statistical manifolds
Hajime Urakawa
https://arxiv.org/abs/2507.13612 https…

The second variational formula of the variational problems for mappings between statistical manifolds
Recently, H. Furuhata and R. Ueno obtained the first variational formula of smooth mappings of a compact statistical manifold into another manifold. In this paper, we show the second variational formula of harmonic mappings of a statistical manifold into another one. Furthermore, we define the stability, the index and the nullity for the mappings, and we show the weakly stability for the harmonic mappings into any statistical manifolds of non-positive curvature. We also give several examples ca…

Wave maps from circle to Riemannian manifold: global controllability is equivalent to homotopy
Jean-Michel Coron, Joachim Krieger, Shengquan Xiang
https://arxiv.org/abs/2509.12779

Wave maps from circle to Riemannian manifold: global controllability is equivalent to homotopy
We study wave maps from the circle to a general compact Riemannian manifold. We prove that the global controllability of this geometric equation is characterized precisely by the homotopy class of the data. As a remarkable intermediate result, we establish uniform-time global controllability between steady states, providing a partial answer to an open problem raised by Dehman, Lebeau and Zuazua (2003). Finally, we obtain quantitative exponential stability around closed geodesics with negative s…

Heat kernel asymptotics and analytic torsion on non-degenerate CR manifolds
Chin-Yu Hsiao, Rung-Tzung Huang, Guokuan Shao
https://arxiv.org/abs/2509.19167 https://

An explicit formula for the Laplace-Beltrami operator on the Stiefel manifold
Petre Birtea, Ioan Casu, Dan Comanescu
https://arxiv.org/abs/2509.18877 https://

On the spectral stability of finite coverings
Werner Ballmann, Sugata Mondal, Panagiotis Polymerakis
https://arxiv.org/abs/2507.17466 https://arxiv.org/pdf…

On the spectral stability of finite coverings
We prove the non-existence of new eigenvalues in $[0,Λ]$ for specific and random finite coverings of a complete and connected Riemannian manifold $M$ of bounded sectional curvature, where $Λ$ is any positive number below the essential spectrum of $M$ and the spectrum of the universal cover of $M$, provided the representation theory of the fundamental group of $M$ satisfies certain conditions.

Positive curvature conditions on contractible manifolds
Paul Sweeney Jr
https://arxiv.org/abs/2507.15719 https://arxiv.org/pdf/2507.1…

Positive curvature conditions on contractible manifolds
Our goal is to identify curvature conditions that distinguish Euclidean space in the case of open, contractible manifolds and the disk in the case of compact, contractible manifolds with boundary. First, we show that an open manifold that is the interior of a sufficiently connected, compact, contractible 5-manifold with boundary and supports a complete Riemannian metric with uniformly positive scalar curvature is diffeomorphic to Euclidean 5-space. Next, we investigate the analogous question fo…

Calabi-Yau locally conformally K\"ahler manifolds
Giuseppe Barbaro, Alexandra Otiman
https://arxiv.org/abs/2509.18364 https://arxiv.org/pdf/2509.18364…

On Hopf's conjecture and positive second intermediate Ricci curvature
Lee Kennard, Lawrence Mouill\'e, Jan Nienhaus
https://arxiv.org/abs/2507.16936 https://

On Hopf's conjecture and positive second intermediate Ricci curvature
Hopf conjectured that even-dimensional closed Riemannian manifolds with positive sectional curvature have positive Euler characteristic. The conclusion of the conjecture is known to fail if the positive sectional curvature assumption is relaxed in any number of ways, including to positive second intermediate Ricci curvature. Here we prove that if a manifold with positive second intermediate Ricci curvature has dimension divisible by four and torus symmetry of rank at least ten, then it has posi…

Parallel torsion and $G_2, Spin(7)$ instantons
Stefan Ivanov, Alexander Petkov, Luis Ugarte
https://arxiv.org/abs/2509.10623 https://arxiv.org/pdf/2509.106…

Parallel torsion and $G_2, Spin(7)$ instantons
Instanton properties of the characteristic connection $\nabla$ on an integrable $G_2$ manifold as well as instanton condition of the torsion connection $\nabla$ on a $Spin(7)$ manifold are investigated. It is shown that for an integrable $G_2$ manifold with $\nabla$-parallel Lee form the curvature of the characteristic connection is a $G_2$ instanton exactly when the torsion 3-form is $\nabla$-parallel. It is observed that on a compact $Spin(7)$ manifold with $\nabla$ closed torsion 3-form the …