Tootfinder

This https://arxiv.org/abs/2409.19626 has been replaced.
link: https://scholar.google.com/scholar?q=a

Three-dimensional Riemannian manifolds associated with locally conformal Riemannian product manifolds
A 3-dimensional Riemannian manifold equipped with a tensor structure of type $(1,1)$, whose fourth power is the identity, is considered. This structure acts as an isometry with respect to the metric. A Riemannian almost product manifold associated with such a manifold is also studied. It turns out, that the almost product manifold belongs to the class of locally conformal Riemannian product manifolds of the Naveira classification. Conditions for the additional structures of the manifolds to be …

Distributed Retraction-Free and Communication-Efficient Optimization on the Stiefel Manifold
Yilong Song, Peijin Li, Bin Gao, Kun Yuan
https://arxiv.org/abs/2506.02879

Distributed Retraction-Free and Communication-Efficient Optimization on the Stiefel Manifold
Optimization problems on the Stiefel manifold, ranging from principal component analysis to enhancing neural network robustness, are ubiquitous in machine learning. The Landing algorithm avoids computationally expensive retraction operations on manifolds, making it highly competitive for large-scale problems. This paper extends this method to distributed settings, introducing *EF-Landing*, the first retraction-free and communication-efficient algorithm for distributed stochastic optimization on…

For all the German speakers in my network: my research on spatial layouts and communication has been featured in a lovely and detailed article in the weekly German newspaper Die Zeit discussing the manifold relations between architecture and social outcomes, ranging from political coalition negotiations to the mutiny on the Bounty, from team meetings in offices to places for living

Architektur: Wie Architekten Gespräche lenken – und Macht verteilen
Gute Architektur verbindet Menschen, schlechte trennt sie. Wer die Gesetze des Bauens kennt, kann Politiker zusammenbringen – und sogar den Lauf der Geschichte verändern.

Regular genus of $\mathbb{S}^2 \times \mathbb{S}^1 \times \mathbb{S}^1$, $4$-torus, and small covers over $\Delta^2 \times \Delta^2$
Anshu Agarwal, Biplab Basak
https://arxiv.org/abs/2506.01315

Regular genus of $\mathbb{S}^2 \times \mathbb{S}^1 \times \mathbb{S}^1$, $4$-torus, and small covers over $Δ^2 \times Δ^2$
A crystallization of a PL manifold is an edge-colored graph encoding a contracted triangulation of the manifold. The concept of regular genus generalizes the notions of surface genus and Heegaard genus for 3-manifolds to higher-dimensional closed PL manifolds. The regular genus of a PL manifold is a PL invariant. Determining the regular genus of a closed PL $n$-manifold remains a fundamental challenge in combinatorial topology. In this article, we first resolve a conjecture by proving that the …

This https://arxiv.org/abs/1804.08452 has been replaced.
link: https://scholar.google.com/scholar?q=a

Two closed geodesics on compact bumpy Finsler manifolds
In this paper, we prove there are at least two closed geodesics on any compact bumpy Finsler $n$-manifold with finite fundamental group and $n\ge 2$. Thus generically there are at least two closed geodesics on compact Finsler manifolds with finite fundamental group. Furthermore, there are at least two closed geodesics on any compact Finsler $2$-manifold, and this lower bound is achieved by the Katok 2-sphere $(S^2, F)$ and 2-real projective space $(S^2/\Z_2, F)$, cf. \cite{Kat}.

Hausdorff Dimension of non-conical and Myrberg limit sets
Mahan Mj, Wenyuan Yang
https://arxiv.org/abs/2506.04955 https://arxiv.org/p…

Hausdorff Dimension of non-conical and Myrberg limit sets
In this paper, we develop techniques to study the Hausdorff dimensions of non-conical and Myrberg limit sets for groups acting on negatively curved spaces. We establish maximality of the Hausdorff dimension of the non-conical limit set of $G$ in the following cases. 1. $M$ is a finite volume complete Riemannian manifold of pinched negative curvature and $G$ is an infinite normal subgroups of infinite index in $π_1(M)$. 2. $G$ acts on a regular tree $X$ with $X/G$ infinite and amenable (dimensi…

This https://arxiv.org/abs/2403.05349 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Extended Sobolev scale for vector bundles, and its applications
We study an extended Sobolev scale for smooth vector bundles over a smooth closed manifold. This scale is built on the base of inner product distribution spaces of generalized smoothness given by an arbitrary positive function OR-varying at infinity. We show that this scale is obtained by the quadratic interpolation (with a function parameter) between inner product Sobolev spaces, is closed with respect to the quadratic interpolation, and consists of all Hilbert spaces that are interpolation sp…

The Latent Space Hypothesis: Toward Universal Medical Representation Learning
Salil Patel
https://arxiv.org/abs/2506.04515 https://ar…

The Latent Space Hypothesis: Toward Universal Medical Representation Learning
Medical data range from genomic sequences and retinal photographs to structured laboratory results and unstructured clinical narratives. Although these modalities appear disparate, many encode convergent information about a single underlying physiological state. The Latent Space Hypothesis frames each observation as a projection of a unified, hierarchically organized manifold -- much like shadows cast by the same three-dimensional object. Within this learned geometric representation, an individ…

Concave symplectic toric fillings
Aleksandra Marinkovi\'c
https://arxiv.org/abs/2506.03912 https://arxiv.org/pdf/2506.03912

Concave symplectic toric fillings
As shown by Etnyre and Honda in [EH], every contact 3-manifold admits infinitely many concave symplectic fillings that are mutually not symplectomorphic and not related by blow ups. In this note we refine this result in the toric setting by showing that every contact toric 3-manifold admits infinitely many concave symplectic toric fillings that are mutually not equivariantly symplectomorphic and not related by blow ups. The concave symplectic toric structure is constructed on certain linear and…

Stable invariant manifold for generalized ODEs with applications to measure differential equations
Lu Weijie, Piccione Paolo, Xia Yonghui
https://arxiv.org/abs/2506.02874

Stable invariant manifold for generalized ODEs with applications to measure differential equations
This paper establishes the stable invariant manifold for a new kind of differential equations defined by Kurzweil integral, so-called {\em generalized ODEs} on a Banach space. The nonlinear generalized ODEs are formulated as $$ \frac{dz}{dτ}=D[Λ(t)z+F(z,t)], $$ where $Λ(t)$ is a bounded linear operator on a Banach space $\mathscr{Z}$ and $F(z,t)$ is a nonlinear Kurzweil integrable function on $\mathscr{Z}$. The letter $D$ represents that generalized ODEs are defined via its solution, and $\f…

Manifolds of mappings associated with real-valued function spaces and natural mappings between them
Matthieu F. Pinaud
https://arxiv.org/abs/2506.03366 htt…

Manifolds of mappings associated with real-valued function spaces and natural mappings between them
Let $M$ be a compact smooth manifold with corners and $N$ be a finite dimensional smooth manifold without boundary which admits local addition. We define a smooth manifold structure to general sets of continuous mapings $\mathcal{F}(M,N)$ whenever functions spaces $\mathcal{F}(U,\mathbb{R})$ on open subsets $U\subseteq [0,\infty)^n$ are given, subject to simple axioms. Construction and properties of spaces of sections and smoothness of natural mappings between spaces $\mathcal{F}(M,N)$ are disc…

This https://arxiv.org/abs/2305.19415 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Euclidean nets under isometric embeddings
Suppose that there exists a discrete subset $X$ of a complete, connected, $n$-dimensional Riemannian manifold $M$ such that the Riemannian distances between points of $X$ correspond to the Euclidean distances of a net in $\mathbb{R}^{n}$. What can then be derived about the geometry of $M$? In arXiv:2004.08621 it was shown that if $n=2$ then $M$ is isometric to $\mathbb{R}^{2}$. In this paper we show two consequential geometric properties that the manifold $M$ shares with the Euclidean space in …

Nakano-Griffiths inequality, holomorphic Morse inequalities, and extension theorems for $q$-concave domains
Bingxiao Liu, George Marinescu, Huan Wang
https://arxiv.org/abs/2506.00879

Nakano-Griffiths inequality, holomorphic Morse inequalities, and extension theorems for $q$-concave domains
We consider a compact $n$-dimensional complex manifold endowed with a holomorphic line bundle that is semi-positive everywhere and positive at least at one point. Additionally, we have a smooth domain of this manifold whose Levi form has at least $n-q$ negative eigenvalues ($1\leq q\leq n-1$) on the boundary. We prove that every $\overline{\partial}_b$-closed $(0,\ell)$-form on the boundary with values in a holomorphic vector bundle admits a meromorphic extension for all $q\leq \ell\leq n-1$. T…

$W$-entropy formulas and Langevin deformation on the $L^q$-Wasserstein space over Riemannian manifolds
Rong Lei, Xiang-Dong Li, Yu-Zhao Wang
https://arxiv.org/abs/2506.01279

$W$-entropy formulas and Langevin deformation on the $L^q$-Wasserstein space over Riemannian manifolds
Inspired by Perelman's seminal work on the $W$-entropy formula for the Ricci flow and related works, we prove the $W$-entropy formula and rigidity theorem for the geodesic flow on the $L^q$-Wasserstein space over a complete Riemannian manifold with bounded geometry condition. Then we introduce the Langevin deformation on the $L^q$-Wasserstein space over a complete Riemannian manifold, which interpolates between the $p$-Laplacian heat equation and the geodesic flow on the $L^q$-Wasserstein space…

This https://arxiv.org/abs/2205.09337 has been replaced.
link: https://scholar.google.com/scholar?q=a

Deep Learning in Business Analytics: A Clash of Expectations and Reality
Our fast-paced digital economy shaped by global competition requires increased data-driven decision-making based on artificial intelligence (AI) and machine learning (ML). The benefits of deep learning (DL) are manifold, but it comes with limitations that have, so far, interfered with widespread industry adoption. This paper explains why DL, despite its popularity, has difficulties speeding up its adoption within business analytics. It is shown that the adoption of deep learning is not only aff…

This https://arxiv.org/abs/2505.23679 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Boundary terms in cosmology
In the derivation of the Einstein field equations via Hamilton's principle, the inclusion of a boundary term is essential to render the variational problem well-posed, as it addresses variations that do not vanish at the boundary of the spacetime manifold. Typically, this term is chosen as the Gibbons-Hawking-York boundary term. In this work, we propose an alternative treatment of the boundary term within a cosmological framework by employing the Lagrange multiplier method. This approach enforc…

Rescaled topological entropy
E. Rego, C. Rojas, X. Wen
https://arxiv.org/abs/2506.02383 https://arxiv.org/pdf/2506.02383

Rescaled topological entropy
We prove that to any smooth vector field of a closed manifold it can be assigned a nonnegative number called {\em rescaled topological entropy} satisfying the following properties: it is an upper bound for both the topological entropy and the rescaled metric entropy \cite{ww}; coincides with the topological entropy for nonsingular vector fields; is positive for certain surface vector fields (in contrast to the topological entropy); is invariant under rescaled topological conjugacy; and serves a…

This https://arxiv.org/abs/2409.06512 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Manifolds of absolutely continuous functions with values in an infinite-dimensional manifold and regularity properties of half-Lie groups
For $p\in [1,\infty]$, we define a smooth manifold structure on the set $AC_{L^p}([a,b],N)$ of absolutely continuous functions $γ\colon [a,b]\to N$ with $L^p$-derivatives for all real numbers $a

This https://arxiv.org/abs/2312.00138 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Scalar curvature and volume entropy of hyperbolic 3-manifolds
We show that any closed hyperbolic 3-manifold M admits a Riemannian metric with scalar curvature at least -6, but with volume entropy strictly larger than 2. In particular, this construction gives counterexamples to a conjecture of I. Agol, P. Storm and W. Thurston.

Strongly driven transmon as an incoherent noise source
Linda Greggio, R\'emi Robin, Mazyar Mirrahimi, Alexandru Petrescu
https://arxiv.org/abs/2505.24549

Strongly driven transmon as an incoherent noise source
Under strong drives, which are becoming necessary for fast high-fidelity operations, transmons can be structurally unstable. Due to chaotic effects, the computational manifold is no longer well separated from the remainder of the spectrum, which correlates with enhanced offset-charge sensitivity and destructive effects in readout. We show here that these detrimental effects can further propagate to other degrees of freedom, for example to neighboring qubits in a multi-qubit system. Specifically…

Logrithmic Versions of Ginzburg's Sharp Operation for Free Divisors
Xia Liao, Xiping Zhang
https://arxiv.org/abs/2505.24236 https://

Logrithmic Versions of Ginzburg's Sharp Operation for Free Divisors
Let $M$ be a complex manifold, $D\subset M$ a free divisor and $U=M\setminus D$ its complement. In this paper we study the characteristic cycle $\textup{CC}(γ\cdot \ind_U)$ of the restriction of a constructible function $γ$ on $U$. We globalise Ginzburg's local sharp construction and introduce the log transversality condition, which is a new transversality condition about the relative position of $γ$ and $D$. We prove that the log transversality condition is satisfied if either $D$ is normal…

Bochner-type theorems for distributional category
Ekansh Jauhari, John Oprea
https://arxiv.org/abs/2505.21763 https://arxiv.org/pdf/2…

Bochner-type theorems for distributional category
We show that in the presence of a geometric condition such as non-negative Ricci curvature, the distributional category of a manifold may be used to bound invariants, such as the first Betti number and macroscopic dimension, from above. Moreover, à la Bochner, when the bound is an equality, special constraints are imposed on the manifold. We show that the distributional category of a space also bounds the rank of the Gottlieb group, with equality imposing constraints on the fundamental group. …

Equivalence of Left- and Right-Invariant Extended Kalman Filters on Matrix Lie Groups
Finn G. Maurer, Erlend A. Basso, Henrik M. Schmidt-Didlaukies, Torleiv H. Bryne
https://arxiv.org/abs/2506.01514

Equivalence of Left- and Right-Invariant Extended Kalman Filters on Matrix Lie Groups
This paper derives the extended Kalman filter (EKF) for continuous-time systems on matrix Lie groups observed through discrete-time measurements. By modeling the system noise on the Lie algebra and adopting a Stratonovich interpretation for the stochastic differential equation (SDE), we ensure that solutions remain on the manifold. The derivation of the filter follows classical EKF principles, naturally integrating a necessary full-order covariance reset post-measurement update. A key contribut…

Maximum volume coordinates for Grassmann interpolation: Lagrange, Hermite, and errors
Rasmus Jensen, Ralf Zimmermann
https://arxiv.org/abs/2506.01574 https…

Maximum volume coordinates for Grassmann interpolation: Lagrange, Hermite, and errors
We present a novel approach to Riemannian interpolation on the Grassmann manifold. Instead of relying on the Riemannian normal coordinates, i.e. the Riemannian exponential and logarithm maps, we approach the interpolation problem with an alternative set of local coordinates and corresponding parameterizations. A special property of these coordinates is that their calculation does not require any matrix decompositions. This is a numerical advantage over Riemann normal coordinates and many other …

A topologically extendible mapping class that is not smoothly extendible
Shital Lawande, Kuldeep Saha
https://arxiv.org/abs/2505.23999 https://

A topologically extendible mapping class that is not smoothly extendible
We give an example of a smooth characteristic embedding of a torus in $\s^2 \times \s^2 \# \s^1 \times \s^3$ such that there exists no diffeomorphism of the ambient $4$-manifold that induces the Dehn twist along a meridian of the torus, but there exists a homeomorphism of the ambient $4$-manifold, isotopic to identity, that induces the Dehn twist. As an application of our methods, we provide examples of two proper smooth embeddings of an annulus in $\s^2 \times \s^2 \# \s^1 \times \s^3 \setminu…

This https://arxiv.org/abs/2104.07431 has been replaced.
link: https://scholar.google.com/scholar?q=a

One-ended spanning subforests and treeability of groups
We show that several new classes of groups are measure strongly treeable. In particular, finitely generated groups admitting planar Cayley graphs, elementarily free groups, and the group of isometries of the hyperbolic plane and all its closed subgroups. This provides the first examples of one-ended nonamenable groups which are measure strongly treeable. In higher dimensions, we also prove a dichotomy that the fundamental group of a closed aspherical $3$-manifold is either amenable or has stron…

Weyl formula improvement for product of Zoll manifolds
Yanfei Wang
https://arxiv.org/abs/2506.02299 https://arxiv.org/pdf/2506.02299

Weyl formula improvement for product of Zoll manifolds
Iosevich and Wyman have proved in ~\cite{IoWy} that the remainder term in classical Weyl law can be improved from $O(λ^{d-1})$ to $o(λ^{d-1})$ in the case of product manifold by using a famous result of Duistermaat and Guillemin. They also showed that we could have polynomial improvement in the special case of Cartesian product of round spheres by reducing the problem to the study of the distribution of weighted integer lattice points. In this paper, we show that we can extend this result to …

Simplicial volume via foliated simplices and duality
Filippo Sarti
https://arxiv.org/abs/2506.02962 https://arxiv.org/pdf/2506.02962

Simplicial volume via foliated simplices and duality
Let $M$ be an aspherical oriented closed connected manifold with universal cover $\widetilde{M}\to M$ and let $Γ=π_1(M)\curvearrowright (X,μ)$ be a measure preserving action on a standard Borel probability space. We consider singular foliated simplices on the measured foliation $Γ\backslash(\widetilde{M}\times X)$ defined by Sauer and we compare the \emph{real singular foliated homology} with classic singular homology. We introduce a notion of \emph{foliated fundamental class} and we prove …

$L^2$-Hodge theory of Hybrid Landau-Ginzburg models of Calabi-Yau complete intersections
Jeehoon Park, Jaewon Yoo
https://arxiv.org/abs/2505.24218 https://…

$L^2$-Hodge theory of Hybrid Landau-Ginzburg models of Calabi-Yau complete intersections
Given a Calabi-Yau smooth projective complete intersection variety $V$ over $\C$, a hybrid Landau-Ginzburg (LG) model may be associated using the Cayley trick. This hybrid LG model comprises a non-compact Calabi-Yau manifold $X_{CY}$, and a holomorphic function $W$, defined on $X_{CY}$, such that the critical locus of $W$ is isomorphic to $V$. We construct a complete Kähler metric $\mathfrak{g}$ and a bounded Calabi-Yau volume form $Ω$ on $X_{CY}$ such that $(X_{CY},\mathfrak{g}, Ω)$ is a bo…

Bernstein-Markov measures and Toeplitz theory
Siarhei Finski
https://arxiv.org/abs/2506.01610 https://arxiv.org/pdf/2506.01610…

Bernstein-Markov measures and Toeplitz theory
We prove that Toeplitz operators associated with a Bernstein-Markov measure on a compact complex manifold endowed with a big line bundle form an algebra under composition. As an application, we derive a Szegő-type spectral equidistribution result for this class of operators. A key component of our approach is the off-diagonal asymptotic analysis of the Bergman kernel, also known as the Christoffel-Darboux kernel.

This https://arxiv.org/abs/2412.05927 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Abstract categorical residues and Calabi-Yau structures
Inspired by the simple fact that a compact n-dimensional manifold-with-boundary which satisfies Poincaré-Lefschetz duality of dimension n has a boundary which itself satisfies Poincaré duality of dimension n, we show that the categorical formal punctured neighborhood of infinity, a canonical categorical construction associated to every $A_{\infty}$ category, has a weak proper Calabi-Yau structure of dimension n-1 whenever the original $A_{\infty}$ category admits a weak smooth Calabi-Yau stru…

This https://arxiv.org/abs/2406.05694 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A Low Rank Neural Representation of Entropy Solutions
We construct a new representation of entropy solutions to nonlinear scalar conservation laws with a smooth convex flux function in a single spatial dimension. The representation is a generalization of the method of characteristics and posseses a compositional form. While it is a nonlinear representation, the embedded dynamics of the solution in the time variable is linear. This representation is then discretized as a manifold of implicit neural representations where the feedforward neural netwo…

Kobayashi-Hitchin Correspondence for Saturated Reflexive Parabolic Sheaves on K\"ahler manifolds
Tianshu Jiang, Jiayu Li
https://arxiv.org/abs/2506.03579

Kobayashi-Hitchin Correspondence for Saturated Reflexive Parabolic Sheaves on Kähler manifolds
In this paper, we study the Kobayashi-Hitchin correspondence in the setting of parabolic sheaves with a simple normal crossing divisor over a compact Kähler manifold using the method of Hermitian-Yang-Mills flow.

Anosov actions: minimality of foliations or suspension action
Rodrigo R. Lopes, Carlos Maquera, R\'egis Var\~ao
https://arxiv.org/abs/2505.24598 https:…

Anosov actions: minimality of foliations or suspension action
We prove that an Anosov action of $\mathbb{R}^k$ over a compact manifold $M$ transitive on regular sub-cones satisfies the dichotomy: each stable and unstable leaf is dense or the Anosov action is topologically conjugated to a suspension of a $\mathbb{Z}^k$-Anosov action. This represents an important progress toward addressing Verjovsky's extended conjecture for Anosov actions, as developed by Barbot and Maquera.

This https://arxiv.org/abs/2502.20923 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Spinning boson stars in nonlinear sigma models and Universal Relations
Boson stars are hypothetical compact objects derived from solutions of a self-gravitating complex scalar field. In this study, we extend the traditional models by generalizing the kinetic term of the scalar field to that of a nonlinear sigma model. Concretely, we obtain spinning boson star solutions for a family of models parametrized by the curvature of their two-dimensional target manifold, as well as for various self-interaction potentials. We derive the global properties and multipolar stru…

This https://arxiv.org/abs/2210.14765 has been replaced.
link: https://scholar.google.com/scholar?q=a

Holed cone structures on 3-manifolds
We introduce holed cone structures on 3-manifolds to generalize cone structures. In the same way as a cone structure, a holed cone structure induces the holonomy representation. We consider the deformation space consisting of the holed cone structures on a 3-manifold whose holonomy representations are irreducible. This deformation space for positive cone angles is a covering space on a reasonable subspace of the character variety.

On families of Finsler metrics
Ismail Saglam (IRMA), Ken'Ichi Ohshika (IRMA), Athanase Papadopoulos (IRMA)
https://arxiv.org/abs/2506.03749 https://

On families of Finsler metrics
In this paper, we answer some natural questions on symmetrisation and more general combinations of Finsler metrics, with a view towards applications to Funk and Hilbert geometries and to metrics on Teichm{ü}ller spaces. For a general non-symmetric Finsler metric on a smooth manifold, we introduce two different families of metrics, containing as special cases the arithmetic and the max symmetrisations respectively of the distance functions associated with these Finsler metrics. We are intereste…

This https://arxiv.org/abs/2307.07774 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Heptagon relations from a simplicial 3-cocycle, and their cohomology
We introduce new algebraic structures associated with heptagon relations -- higher analogue of the well-known pentagon. The main points we deal with are: (i) polygon relations as algebraic imitations of Pachner moves, on the example of heptagon, (ii) parameterization of heptagon relations by simplicial 3-cocycles, (iii) applications to invariants of pairs "piecewise linear 5-manifold, a 3rd cohomology class on it".

Information Geometry on the $\ell^2$-Simplex via the $q$-Root Transform
Levin Maier
https://arxiv.org/abs/2506.00485 https://arxiv.or…

Information Geometry on the $\ell^2$-Simplex via the $q$-Root Transform
In this paper, we introduce \emph{$\ell^p$-information geometry}, an infinite dimensional framework that shares key features with the geometry of the space of probability densities \( \mathrm{Dens}(M) \) on a closed manifold, while also incorporating aspects of measure-valued information geometry. We define the \emph{$\ell^2$-probability simplex} with a noncanonical differentiable structure induced via the \emph{$q$-root transform} from an open subset of the $\ell^p$-sphere. This structure rend…

This https://arxiv.org/abs/2108.12000 has been replaced.
link: https://scholar.google.com/scholar?q=a

Hyperbolic models of transitive topologically Anosov flows in dimension three
We prove that every transitive topologically Anosov flow on a closed 3-manifold is orbitally equivalent to a smooth Anosov flow, preserving an ergodic smooth volume form.

On compact sets possessing $q$-convex functions
Thomas Pawlaschyk, Nikolay Shcherbina
https://arxiv.org/abs/2505.24588 https://arxiv.…

On compact sets possessing $q$-convex functions
We show that there exists a $q$-convex function in a neighborhood of a compact set $K$ in a complex manifold $\mathcal{M}$ if and only if the $q$-nucleus of this compact set is empty. The latter can be characterized as the maximal $q$-pseudoconcave subset of $K$, i.e., a subset of $K$ containing all other compact $q$-pseudoconcave subsets in $K$.

Hyperbolic small knots in spherical manifolds
Kazuhiro Ichihara
https://arxiv.org/abs/2506.01041 https://arxiv.org/pdf/2506.01041

Hyperbolic small knots in spherical manifolds
It was conjectured by Lopez that every closed irreducible non-Haken 3-manifold contains a small knot. In this paper, we give explicit examples of hyperbolic small knots in most closed orientable spherical 3-manifolds other than prism manifolds.

This https://arxiv.org/abs/2505.08280 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Extremising eigenvalues of the GJMS operators in a fixed conformal class
Let $(M,g)$ be a closed Riemannian manifold of dimension $n\geq 3$. If $s$ is a positive integer satisfying $2s

This https://arxiv.org/abs/2410.08902 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Residual finiteness of some automorphism groups of high dimensional manifolds
We show that for a smooth, closed 2-connected manifold $M$ of dimension $d \geq 6$, the topological mapping class group $π_0 \mathrm{Homeo}(M)$ is residually finite, in contrast to the situation for the smooth mapping class group $π_0 \mathrm{Diff}(M)$. Combined with a result of Sullivan, this implies that $π_0 \mathrm{Homeo}(M)$ is an arithmetic group. The proof uses embedding calculus, and is of independent interest: we show that the $T_k$-mapping class group, $π_0 T_k \mathrm{Diff}(M)$, …

This https://arxiv.org/abs/2412.11103 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Counting Minimal Tori In Riemannian Manifolds
In this paper, we introduce a function which counts minimal tori in a Riemann manifold $(M, g)$ with $\mathrm{dim}\, M \ge 6$. Moreover, we show that this count function is invariant under perturbations of the metric.

This https://arxiv.org/abs/2504.15207 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Parametric Gromov width of Liouville domains
The classical Gromov width measures the largest symplectic ball embeddable into a symplectic manifold; inspired by the symplectic camel problem, we generalize this to ask how large a symplectic ball can be embedded as a family over a parameter space $N$. Given a smooth map $f: N \to Ω$, where $Ω$ is a symplectic manifold, we define the \emph{parametric Gromov width} $\mathrm{Gr}(f,Ω)$ as the supremum of capacities $a>0$ for which there exists a family of balls, parametrized by $N$, of capaci…

This https://arxiv.org/abs/2501.18584 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Corks, exotic 4-manifolds and genus functions
We prove that every 4-dimensional oriented handlebody without 3- and 4-handles can be modified to admit infinitely many exotic smooth structures, and further that their genus functions are pairwise equivalent. We furthermore show that, for any 4-manifold admitting an embedding into a symplectic 4-manifold with weakly convex boundary, its genus function is algebraically realized as those of infinitely many pairwise exotic 4-manifolds. We also prove that, for any two 4-manifolds with non-degenera…

Homology manifolds and homogeneous compacta
Vesko Valov
https://arxiv.org/abs/2505.07196 https://arxiv.org/pdf/2505.07196

Homology manifolds and homogeneous compacta
A non-trivial separable metric space $X$ is called an almost homology $n$-manifold if the homology groups $H_k(X,X\backslash\{x\},\mathbb Z)$ are trivial for all $x\in X$ and all $k=0,1,..,n-1$. We provide a necessary and sufficient condition locally compact homogeneous $ANR$-spaces or strongly locally homogeneous $ANR$-spaces to be almost homology $n$-manifolds.

Amalgamations along surfaces with boundary in a handlebody
Siqi Ding, Fengchun Lei, Wei Lin, Andrei Vesnin
https://arxiv.org/abs/2505.22530 https://…

Amalgamations along surfaces with boundary in a handlebody
Let M be a connected orientable 3-manifold, and F a compact connected orientable surface properly embedded in M. If F cuts M into two connected 3-manifolds X and Y, that is, M=X \cup_F Y, we say that M is an amalgamation of X and Y along F; and if F cuts M into a connected 3-manifold X, we say that M is a self-amalgamation of X along F. A characterization of an amalgamation of two handlebodies along a surface, incompressible in both, to be a handlebody was obtained by Lei, Liu, Li, and Vesnin. …

This https://arxiv.org/abs/2411.03277 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Asymptotic stability equals exponential stability -- while you twist your eyes
Suppose that two vector fields on a smooth manifold render some equilibrium point globally asymptotically stable (GAS). We show that there exists a homotopy between the corresponding semiflows such that this point remains GAS along this homotopy.

This https://arxiv.org/abs/2209.05806 has been replaced.
link: https://scholar.google.com/scholar?q=a

The Weyl tube theorem for Kähler manifolds
As sharpened in terms of Alesker's theory of valuations on manifolds, a classic theorem of Weyl asserts that the coefficients of the tube polynomial of an isometrically embedded riemannian manifold $M \hookrightarrow \mathbb R^n$ constitute a canonical finite dimensional subalgebra $\mathcal {L K}(M)$ of the algebra $\mathcal{V} (M)$ of all smooth valuations on $M$, isomorphic to the algebra of valuations on Euclidean space that are invariant under rigid motions. We construct an analogous, larg…

Ideal Triangulations and Once-Punctured Surface Bundles
Birch Bryant
https://arxiv.org/abs/2505.21798 https://arxiv.org/pdf/2505.2179…

Ideal Triangulations and Once-Punctured Surface Bundles
A well-known result of Walsh states that if $\mathcal T^*$ is an ideal triangulation of an atoroidal, acylindrical, irreducible, compact 3-manifold with torus boundary components, then every properly embedded, two-sided, incompressible surface $S$ is isotopic to a spun-normal surface unless $S$ is isotopic to a fiber or virtual fiber. Previously it was unknown if for such a 3-manifold an ideal triangulation in which a fiber spun-normalizes exists. We give a proof of existence and give an algori…

This https://arxiv.org/abs/2111.14528 has been replaced.
link: https://scholar.google.com/scholar?q=a

Reconstruction and interpolation of manifolds II: Inverse problems with partial data for distances observations and for the heat kernel
We consider how a closed Riemannian manifold $M$ and its metric tensor $g$ can be approximately reconstructed from local distance measurements. Moreover, we consider an inverse problem of determining $(M,g)$ from limited knowledge on the heat kernel. In the part 1 of the paper, we considered the approximate construction of a smooth manifold in the case when one is given the noisy distances $\tilde d(x,y)=d(x,y)+\varepsilon_{x,y}$ for all points $x,y\in X$, where $X$ is a $δ$-dense subset of $M…

This https://arxiv.org/abs/2409.11931 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The space of totally real flat minimal surfaces in the Quaternionic projective space HP^3
We prove that the moduli space of all noncongruent linearly full totally real flat minimal immersions from the complex plane C into HP^3 that do not lie in CP^3 has three components, each of which is a manifold of real dimension 6. As an application, we give a description of the moduli space of all noncongruent linearly full totally real flat minimal tori in HP^3 that do not lie in CP^3.

This https://arxiv.org/abs/2504.19731 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Tian's theorem for Grassmannian embeddings and degeneracy sets of random sections
Let $(X,ω)$ be a compact Kähler manifold, $(L,h^L)$ be a positive line bundle, and $(E,h^E)$ be a Hermitian holomorphic vector bundle of rank $r$ on $X$. We prove that the pullback by the Kodaira embedding associated to $L^p\otimes E$ of the $k$-th Chern class of the dual of the universal bundle over the Grassmannian converges as $p\to\infty$ to the $k$-th power of the Chern form $c_1(L,h^L)$, for $0\leq k\leq r$. If $c_1(L,h^L)=ω$ we also determine the second term in the semiclassical expan…

This https://arxiv.org/abs/2505.13114 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A Kahlerian approche to the Schrodinger equation in Siegel jacobi Space of the lognormal distribution
In this paper, we describe the evolution of spectral curves in the Siegel Jacobi space through the Schrodinger equation constructed from a Kahler geometry induced on the lognormal statistical manifold via Dombrowski's construction. We introduce new holomorphic structures and show that the Hamiltonian vector field coincides with the fundamental vector field generated by holomorphic isometries. We construct the time dependent Schrodinger equation from this geometric setting and show that the asso…

This https://arxiv.org/abs/2503.18031 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

$\ast$-$η$-Ricci solitons and Einstein metrics on a weak $β$-Kenmotsu manifold
Weak almost contact manifolds (i.e., the complex structure on the contact distribution is replaced by a nonsingular skew-symmetric tensor), defined by the author and R. Wolak, allow a new look at the classical theory. An important case of these manifolds, which is locally a twisted or warped product, is a weak $β$-Kenmotsu manifold defined by the author and D.S. Patra. In the paper, the concept of the $*$-Ricci tensor is adapted to weak almost contact manifolds, the interaction of the $*$-$η$…

This https://arxiv.org/abs/2505.19181 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Constant Harmonic Mean Curvature Foliation in Asymptotic Schwarzschild Spaces-II
This paper extends the results of [GLS24], where the existence of a constant harmonic mean curvature foliation was established in the setting of a 3-dimensional asymptotically Schwarzschild manifold. Here, we generalize this construction to higher dimensions, proving the existence of foliations by constant harmonic mean curvature hypersurfaces in an asymptotically Schwarzschild manifold of arbitrary dimension. Furthermore, in 3 dimensional case, we demonstrate the local uniqueness of this folia…

This https://arxiv.org/abs/2212.11928 has been replaced.
link: https://scholar.google.com/scholar?q=a

The Gauss formulas for Laplacians on submanifolds
There are several types of Laplacians of a vector field on a Riemannian manifold. These include the Bochner and the Hodge Laplacian. The Gauss formula for the Levi-Civita connection relates the extrinsic connection to the intrinsic connection. We extend the Gauss formula for the connection to formulas for the different types of Laplacians of a vector field on a submanifold of any codimension $k\geq 1$. In the process, we derive a Gauss formula for the Ricci operator, formulas for the divergence…

This https://arxiv.org/abs/2504.19332 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Reeb orbits frequently intersecting a symplectic surface
Consider a symplectic surface in a three-dimensional contact manifold with boundary on Reeb orbits (periodic orbits of the Reeb vector field). We assume that the rotation numbers of the boundary Reeb orbits satisfy a certain inequality, and we also make a technical assumption that the Reeb vector field has a particular ``nice'' form near the boundary of the surface. We then show that there exist Reeb orbits which intersect the interior of the surface, with a lower bound on the frequency of thes…

This https://arxiv.org/abs/2311.07309 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Non-singular extensions of circle-valued Morse functions
In this paper, we consider the non-singular extension problem for circle-valued Morse functions on closed orientable surfaces. The problem asks, given a circle-valued Morse function $f\colon M\to S^{1}$ on a closed orientable surface $M$, under what condition there exist a compact orientable 3-dimensional manifold $N$ with $\partial N = M$ and a submersion $G\colon N \to S^{1}$ such that $G|_{\partial N}=f$. We provide necessary and sufficient conditions for the existence of a non-singular…

Symplectic semi-characteristics
Hao Zhuang
https://arxiv.org/abs/2505.14496 https://arxiv.org/pdf/2505.14496

Symplectic semi-characteristics
We study the symplectic semi-characteristic of a 4n-dimensional closed symplectic manifold. First, we define the symplectic semi-characteristic using the mapping cone complex model of the primitive cohomology. Second, using a vector field with nondegenerate zero points, we prove a counting formula for the symplectic semi-characteristic. As corollaries, we obtain an Atiyah type vanishing property and the fact that the symplectic semi-characteristic is independent of the choices of symplectic for…

This https://arxiv.org/abs/2406.10866 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

K-contact manifolds with minimal closed Reeb orbits
We use the Boothby-Wang fibration to construct certain simply connected K-contact manifolds and we give sufficient and necessary conditions on when such K-contact manifolds are homeomorphic to the odd dimensional spheres. If the symplectic base manifold of the fibration admits a Hamiltonian torus action, we show that on the total space of the fibration, other than the regular K-contact structures which have infinitely many closed Reeb orbits, there are K-contact structures whose closed Reeb orb…

This https://arxiv.org/abs/2309.10997 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the Gromov-Hausdorff limits of Tori with Ricci conditions
Let $n\geq 4$. In this paper, we construct a sequence of smooth Riemannian metrics $g_i $ on $\mathbb{R}^n$ such that: (1) $g_i = g_{\rm Euc} $ outside the standard Euclidean unit ball $B_1 (0) \subset \mathbb{R}^n $, (2) ${\rm Ric}_{g_i} \geq -Λ$ and $ {\rm diam} \left( B_1 (0) ,g_i \right) \leq D $ for some $Λ,D>0$ independent of $i$, (3) The pointed Gromov-Hausdorff limit of $(\mathbb{R}^n ,g_i) $ is a topological orbifold but not a topological manifold. As a consequence, for $n\geq 4$, …

On isomorphisms of semi-free Hamiltonian $S^1$-manifolds and fixed point data
Liat Kessler, Nikolas Wardenski
https://arxiv.org/abs/2505.14000 https://

On isomorphisms of semi-free Hamiltonian $S^1$-manifolds and fixed point data
Following Gonzales, we answer the question of whether the isomorphism type of a semi-free Hamiltonian $S^1$-manifold of dimension six is determined by certain data on the critical levels. We first give counter examples showing that Gonzales' assumptions are not sufficient for a positive answer. Then we prove that it is enough to further assume that the reduced spaces of dimension four are symplectic rational surfaces and the interior fixed surfaces are restricted to at most one level. The addit…