Tootfinder

1.2
I've been on a Zen retreat this week, north of Asheville, NC. I took this picture today of a moth on a window. An images search informs me it's a Tulip-Tree Beauty moth, and it's a member of the "geometer" family of moths. It hadn't occurred to me that "geometry" literally means "to measure the earth." That family of moths are so named because their caterpillars are inch-worms.
🙂 🙏

This https://arxiv.org/abs/2406.07776 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The $L^1$-$L^\infty$-geometry of Teichmüller space -- Second order infinitesimal structures --
The $L^1$-$L^\infty$ geometry is the Finsler geometry of the Teichmüller space by the Teichmüller metric and the $L^1$-norm function of holomorphic quadratic differentials. In this paper, aiming to develop the $L^1$-$L^\infty$-geometry and the differential geometry on the Teichmüller space, we formulate the second order infinitesimal structures (the infinitesimal structures on the (co)tangent bundles) over the Teichmüller space. We will give model spaces of the second order infinitesimal sp…

This https://arxiv.org/abs/2401.16897 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Hamiltonian integrable systems in a magnetic field and Symplectic-Haantjes geometry
We investigate the geometry of classical Hamiltonian systems immersed in a magnetic field in three-dimensional Riemannian configuration spaces. We prove that these systems admit non-trivial symplectic-Haantjes manifolds, which are symplectic manifolds endowed with an algebra of Haantjes (1,1)-tensors. These geometric structures allow us to determine separation variables for known systems algorithmically; besides, the underlying Stäckel geometry is used to construct new families of integrable H…

Accretion Geometry of GX 339-4 in the Hard State: AstroSat View
Swadesh Chand, Gulab C. Dewangan, Andrzej A. Zdziarski, Dipankar Bhattacharya, N. P. S. Mithun, Santosh V. Vadawale
https://arxiv.org/abs/2406.10607

Accretion Geometry of GX 339-4 in the Hard State: AstroSat View
We perform broadband ($0.7-100$ keV) spectral analysis of five hard state observations of the low-mass back hole X-ray binary GX~339--4 taken by AstroSat during the rising phase of three outbursts from $2019$ to $2022$. We find that the outburst in 2021 was the only successful/full outburst, while the source was unable to make transition to the soft state during the other two outbursts in 2019 and 2022. Our spectral analysis employs two different model combinations, requiring two separate Compt…

This https://arxiv.org/abs/2302.14810 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Effective formulas for the geometry of normal homogeneous spaces. Application to flag manifolds
Consider a smooth manifold and an action on it of a compact connected Lie group with a bi-invariant metric. Then, any orbit is an embedded submanifold that is isometric to a normal homogeneous space for the group. In this paper, we establish new explicit and intrinsic formulas for the geometry of any such orbit. We derive our formula of the Levi-Civita connection from an existing generic formula for normal homogeneous spaces, i.e. which determines, a priori only theoretically, the connection. W…

This https://arxiv.org/abs/2406.01466 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

A Matrix Model Proposal for Quantum Gravity and the Quantum Mechanics of Black Holes
We propose a quantum mechanical theory of quantum spaces described by large $N$ noncommutative geometry as a model for quantum gravity. The theory admits fuzzy sphere as static solution. Over the fuzzy geometry, the quantum mechanics of the fermions is given by a sum of oscillators with equal frequency. The energy state where exactly half of the Fermi sea is filled contains the maximal amount of degeneracy. This state of the fuzzy sphere obeys the mass-radius relation of a Schwarzschild black h…

This https://arxiv.org/abs/2406.08920 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csSD_…

AV-GS: Learning Material and Geometry Aware Priors for Novel View Acoustic Synthesis
Novel view acoustic synthesis (NVAS) aims to render binaural audio at any target viewpoint, given a mono audio emitted by a sound source at a 3D scene. Existing methods have proposed NeRF-based implicit models to exploit visual cues as a condition for synthesizing binaural audio. However, in addition to low efficiency originating from heavy NeRF rendering, these methods all have a limited ability of characterizing the entire scene environment such as room geometry, material properties, and the …

This https://arxiv.org/abs/2401.16897 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Hamiltonian integrable systems in a magnetic field and Symplectic-Haantjes geometry
We investigate the geometry of classical Hamiltonian systems immersed in a magnetic field in three-dimensional Riemannian configuration spaces. We prove that these systems admit non-trivial symplectic-Haantjes manifolds, which are symplectic manifolds endowed with an algebra of Haantjes (1,1)-tensors. These geometric structures allow us to determine separation variables for known systems algorithmically; besides, the underlying Stäckel geometry is used to construct new families of integrable H…

A Gentle Introduction to CAT(0) Spaces
S{\o}ren Poulsen
https://arxiv.org/abs/2406.09883 https://arxiv.org/pdf/2406.09883

A Gentle Introduction to CAT(0) Spaces
In this project we explore the geometry of general metric spaces, where we do not necessarily have the tools of differential geometry on our side. Some metric spaces (X,d) allow us to define geodesics, permitting us to compare geodesic triangles in (X,d) to geodesic triangles in a so called model space. In Chapters 1 and 2 we first discuss how to define the length of curves, and geodesics on (X,d), and then using these to portray the notion of ``non-positive curvature'' for a metric space. Chap…

Physically Embodied Gaussian Splatting: A Realtime Correctable World Model for Robotics
Jad Abou-Chakra, Krishan Rana, Feras Dayoub, Niko S\"underhauf
https://arxiv.org/abs/2406.10788

Physically Embodied Gaussian Splatting: A Realtime Correctable World Model for Robotics
For robots to robustly understand and interact with the physical world, it is highly beneficial to have a comprehensive representation - modelling geometry, physics, and visual observations - that informs perception, planning, and control algorithms. We propose a novel dual Gaussian-Particle representation that models the physical world while (i) enabling predictive simulation of future states and (ii) allowing online correction from visual observations in a dynamic world. Our representation co…

[2024-06-17 Mon (UTC), 10 new articles found for math.AG Algebraic Geometry]

This https://arxiv.org/abs/2402.03058 has been replaced.
link: https://scholar.google.com/scholar?q=a

Array Geometry-Robust Attention-Based Neural Beamformer for Moving Speakers
Although mask-based beamforming is a powerful speech enhancement approach, it often requires manual parameter tuning to handle moving speakers. Recently, this approach was augmented with an attention-based spatial covariance matrix aggregator (ASA) module, enabling accurate tracking of moving speakers without manual tuning. However, the deep neural network model used in this module is limited to specific microphone arrays, necessitating a different model for varying channel permutations, number…

[2024-06-18 Tue (UTC), 1 new article found for math.SG Symplectic Geometry]

[2024-06-17 Mon (UTC), 1 new article found for cs.CG Computational Geometry]

This https://arxiv.org/abs/2406.03353 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Quasinormal Modes in Noncommutative Schwarzschild Black Holes: A Spectral Analysis
We present a comprehensive analysis of quasinormal modes (QNMs) for noncommutative geometry-inspired Schwarzschild black holes, encompassing both non-extreme and extreme cases. By employing a spectral method, we calculate the QNMs in the context of scalar, electromagnetic, and gravitational perturbations. Our findings not only challenge previous claims in the literature regarding the instability of these black holes but also reveal remarkable stability for both non-extreme and extreme Schwarzsc…

This https://arxiv.org/abs/2405.15168 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Time evolution of two-point function in expanding universes
By applying the braneworld model, we investigate the time evolution of two-point functions holographically in expanding universes. In order to explain the FLRW cosmologies, we take into account a $p$-brane gas geometry. When we take the boundary of a $p$-brane gas geometry as the braneworld we are living in, $p$-branes are detected as $(p-1)$-dimensional objects to an observer living in the braneworld. These objects lead to the FLRW cosmology which is related to the radial motion of the branewo…

This https://arxiv.org/abs/2404.13705 has been replaced.
initial toot: https://mastoxiv.page/@…

Controlling quantum vortex dynamics and vortex-antivortex annihilation in Bose-Einstein condensates with optical lattices
Superfluids with strong spatial modulation can be experimentally produced in the area of cold atoms under the influence of optical lattices. Here we address $^{87}$Rb bosons at T=0 K in a flat geometry under the influence of a periodic potential with the Gross-Pitaevskii theory. The statics and dynamics of vortex excitations are studied in the case of one dimensional (1D) and of two dimensional (2D) optical lattices, as function of the intensity of the optical lattice. We compute how the vortex…

Kibble-Zurek Mechanism and Beyond: Lessons from a Holographic Superfluid Disk
Chuan-Yin Xia, Hua-Bi Zeng, Andr\'as Grabarits, Adolfo del Campo
https://arxiv.org/abs/2406.09433

Kibble-Zurek Mechanism and Beyond: Lessons from a Holographic Superfluid Disk
The superfluid phase transition dynamics and associated spontaneous vortex formation with the crossing of the critical temperature in a disk geometry is studied in the framework of the $AdS/CFT$ correspondence by solving the Einstein-Abelian-Higgs model in an $AdS_4$ black hole. For a slow quench, the vortex density admits a universal scaling law with the cooling rate as predicted by the Kibble-Zurek mechanism (KZM), while for fast quenches, the density shows a universal scaling behavior as a f…

This https://arxiv.org/abs/2308.05562 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Spectral gap and character limits in arithmetic groups
We establish vanishing results for limits of characters in various discrete groups, most notably irreducible lattices in higher rank semisimple Lie groups. As an application, we show that any sequence of finite-dimensional representations converges to the regular representation in the Fell topology. We achieve this by studying the geometry of the simplex of traces of discrete groups having Kazhdan's property (T) or its relative generalizations.

On the Weak Lefschetz Property for certain ideals generated by powers of linear forms
Giuseppe Favacchio, Juan Migliore
https://arxiv.org/abs/2406.09571 ht…

On the Weak Lefschetz Property for certain ideals generated by powers of linear forms
Ideals $I\subseteq R=k[\mathbb P^n]$ generated by powers of linear forms arise, via Macaulay duality, from sets of fat points $X\subseteq \mathbb P^n$. Properties of $R/I$ are connected to the geometry of the corresponding fat points. When the linear forms are general, many authors have studied the question of whether or not $R/I$ has the Weak Lefschetz Property (WLP). We study this question instead for ideals coming from a family of sets of points called grids. We give a complete answer in the…

A Calibration Approach for Elasticity Estimation with Medical Tools
Sarah Grube, Maximilian Neidhardt, Anna-Katarina Herrmann, Johanna Sprenger, Kian Abdolazizi, Sarah Latus, Christian J. Cyron, Alexander Schlaefer
https://arxiv.org/abs/2406.09947

A Calibration Approach for Elasticity Estimation with Medical Tools
Soft tissue elasticity is directly related to different stages of diseases and can be used for tissue identification during minimally invasive procedures. By palpating a tissue with a robot in a minimally invasive fashion force-displacement curves can be acquired. However, force-displacement curves strongly depend on the tool geometry which is often complex in the case of medical tools. Hence, a tool calibration procedure is desired to directly map force-displacement curves to the corresponding…

This https://arxiv.org/abs/2401.12367 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Unique continuation at infinity: Carleman estimates on general warped cylinders
We obtain a vanishing result for solutions of the inequality $|Δu|\le q_1|u|+q_2|\nabla u|$ that decay to zero along a very general warped cylindrical end of a Riemannian manifold. The appropriate decay condition at infinity on $u$ is related to the behavior of the potential functions $q_1$ and $q_2$ and to the asymptotic geometry of the end. The main ingredient is a new Carleman estimate of independent interest. Geometric applications to conformal deformations an…

This https://arxiv.org/abs/2405.10578 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csSC_…

Jacobi Stability Analysis for Systems of ODEs Using Symbolic Computation
The classical theory of Kosambi-Cartan-Chern (KCC) developed in differential geometry provides a powerful method for analyzing the behaviors of dynamical systems. In the KCC theory, the properties of a dynamical system are described in terms of five geometrical invariants, of which the second corresponds to the so-called Jacobi stability of the system. Different from that of the Lyapunov stability that has been studied extensively in the literature, the analysis of the Jacobi stability has been…

A Gentle Introduction to CAT(0) Spaces
S{\o}ren Poulsen
https://arxiv.org/abs/2406.09883 https://arxiv.org/pdf/2406.09883

A Gentle Introduction to CAT(0) Spaces
In this project we explore the geometry of general metric spaces, where we do not necessarily have the tools of differential geometry on our side. Some metric spaces (X,d) allow us to define geodesics, permitting us to compare geodesic triangles in (X,d) to geodesic triangles in a so called model space. In Chapters 1 and 2 we first discuss how to define the length of curves, and geodesics on (X,d), and then using these to portray the notion of ``non-positive curvature'' for a metric space. Chap…

This https://arxiv.org/abs/2308.09282 has been replaced.
initial toot: https://mastoxiv.page/@a…

Symmetry, topology, and geometry: The many faces of the topological magnetoelectric effect
A delicate tension complicates the relationship between the topological magnetoelectric effect (TME) in three-dimensional (3D) $\mathbb{Z}_2$ topological insulators (TIs) and time-reversal symmetry (TRS). TRS underlies a particular $\mathbb{Z}_2$ topological classification of the electronic ground state of crystalline band insulators and the associated quantization of the magnetoelectric response coefficient calculated using bulk linear response theory but, according to standard symmetry argume…

This https://arxiv.org/abs/2401.00929 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csRO_…

GenH2R: Learning Generalizable Human-to-Robot Handover via Scalable Simulation, Demonstration, and Imitation
This paper presents GenH2R, a framework for learning generalizable vision-based human-to-robot (H2R) handover skills. The goal is to equip robots with the ability to reliably receive objects with unseen geometry handed over by humans in various complex trajectories. We acquire such generalizability by learning H2R handover at scale with a comprehensive solution including procedural simulation assets creation, automated demonstration generation, and effective imitation learning. We leverage larg…

This https://arxiv.org/abs/2106.11479 has been replaced.
link: https://scholar.google.com/scholar?q=a

Differential forms and cohomology in tropical and complex geometry
Ducros, Hrushovski, and Loeser gave maps from families of archimedean diffrential forms to non-archiemedean (or tropical) ones, which are compatible with integrals on algebraic varieties. In this paper, we introduce slight modifications of their maps for complex projective varieties which give natural maps from tropical to the usual Dolbeault cohomology. We also show that our maps are compatible with integrals on generic semi-algebraic subsets and those on their weighted tropicalizations. Weigh…

This https://arxiv.org/abs/2201.11363 has been replaced.
link: https://scholar.google.com/scholar?q=a

The magnitude and spectral geometry
We study the geometric significance of Leinster's notion of magnitude for a smooth manifold with boundary of arbitrary dimension, motivated by open questions for the unit disk in $\mathbb{R}^2$. For a large class of distance functions, including embedded submanifolds of Euclidean space and Riemannian manifolds satisfying a technical condition, we show that the magnitude function is well defined for $R\gg 0$ and admits a meromorphic continuation to sectors in $\mathbb{C}$. In the semiclassical l…

[2024-06-17 Mon (UTC), 1 new article found for cs.CG Computational Geometry]

Hyperbolic embedding of brain networks as a tool for epileptic seizures forecasting
Martin Guillemaud, Louis Cousyn, Vincent Navarro, Mario Chavez
https://arxiv.org/abs/2406.10184

Hyperbolic embedding of brain networks as a tool for epileptic seizures forecasting
The evidence indicates that intracranial EEG connectivity, as estimated from daily resting state recordings from epileptic patients, may be capable of identifying preictal states. In this study, we employed hyperbolic embedding of brain networks to capture non-trivial patterns that discriminate between connectivity networks from days with (preictal) and without (interictal) seizure. A statistical model was constructed by combining hyperbolic geometry and machine learning tools, which allowed fo…

This https://arxiv.org/abs/2401.12367 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Unique continuation at infinity: Carleman estimates on general warped cylinders
We obtain a vanishing result for solutions of the inequality $|Δu|\le q_1|u|+q_2|\nabla u|$ that decay to zero along a very general warped cylindrical end of a Riemannian manifold. The appropriate decay condition at infinity on $u$ is related to the behavior of the potential functions $q_1$ and $q_2$ and to the asymptotic geometry of the end. The main ingredient is a new Carleman estimate of independent interest. Geometric applications to conformal deformations an…

This https://arxiv.org/abs/2311.02753 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

Very Local Impact on the Spectrum of Cosmic-Ray Nuclei below 100 TeV
Recent measurements of primary and secondary CR spectra, their arrival directions, and our improved knowledge of the magnetic field geometry around the heliosphere allow us to set a bound on the distance beyond which a puzzling 10-TeV ``bump'' and certain related spectral features \emph{cannot} originate. The sharpness of the spectral breaks associated with the bump, the abrupt change of the CR intensity across the local magnetic equator ($90^{\circ}$ pitch angle), and the similarity between th…

Interactive Graph Visualization in DDLab
Andrew Wuensche
https://arxiv.org/abs/2406.10704 https://arxiv.org/pdf/2406.10704

Interactive Graph Visualization in DDLab
Interactive visualization of the basin of attraction field, the ``ibaf-graph'', is a new feature in DDLab with the same interactive functions as the ``network-graph'' and ``jump-graph''. These functions allow any node and its connected fragment to be dragged/dropped with the pointer as a graphic animation with elastic links. The fragment itself depends on the node's link setting by inputs, outputs, or either, and a distance in link-steps. Further options include graph geometry, rescaling, node …

A Novel Perspective on Ideal Chern Bands with Strong Short-Range Repulsion: Applications to Correlated Metals, Superconductivity, and Topological Order
Patrick H. Wilhelm, Andreas M. L\"auchli, Mathias S. Scheurer
https://arxiv.org/abs/2406.09505

A Novel Perspective on Ideal Chern Bands with Strong Short-Range Repulsion: Applications to Correlated Metals, Superconductivity, and Topological Order
Motivated by recent experiments on twisted van der Waals materials, we perform an analytical and numerical study of the effects of strong on-site and short-range interactions in fractionally filled ideal Chern bands. We uncover an extensive non-trivial ground state manifold within the band filling range $0 < ν< 1$ and introduce a general principle, the ''three-rule'', for combining flatband wave functions, which governs their zero-energy property on the torus geometry. Based on the structure o…

[2024-06-17 Mon (UTC), no new articles found for math.SG Symplectic Geometry]

Graspness Discovery in Clutters for Fast and Accurate Grasp Detection
Chenxi Wang, Hao-Shu Fang, Minghao Gou, Hongjie Fang, Jin Gao, Cewu Lu
https://arxiv.org/abs/2406.11142

Graspness Discovery in Clutters for Fast and Accurate Grasp Detection
Efficient and robust grasp pose detection is vital for robotic manipulation. For general 6 DoF grasping, conventional methods treat all points in a scene equally and usually adopt uniform sampling to select grasp candidates. However, we discover that ignoring where to grasp greatly harms the speed and accuracy of current grasp pose detection methods. In this paper, we propose "graspness", a quality based on geometry cues that distinguishes graspable areas in cluttered scenes. A look-ahead searc…

A Continuum Erd\H{o}s-Beck Theorem
Paige Bright, Caleb Marshall
https://arxiv.org/abs/2406.10058 https://arxiv.org/pdf/2406.10058

A Continuum Erdős-Beck Theorem
We prove a version of the Erdős--Beck Theorem from discrete geometry for fractal sets in all dimensions. More precisely, let $X\subset \mathbb{R}^n$ Borel and $k \in [0, n-1]$ be an integer. Let $\dim (X \setminus H) = \dim X$ for every $k$-dimensional hyperplane $H \in \mathcal{A}(n,k)$, and let $\mathcal L(X)$ be the set of lines that contain at least two distinct points of $X$. Then, a recent result of Ren shows $$ \dim \mathcal{L}(X) \geq \min \{2 \dim X, 2k\}. $$ If we instead have …

[2024-06-18 Tue (UTC), 4 new articles found for math.MG Metric Geometry]

[2024-06-17 Mon (UTC), 5 new articles found for math.DG Differential Geometry]

This https://arxiv.org/abs/2403.13810 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

The Majorana Hopping and Constraints in the Anti-de Sitter Spacetime
Comformally flat spacetime converts the Anti-de Sitter (AdS) spacetime into a z-dependent metric. We take advantage of this metric to solve Dirac equations in the AdS geometry analytically, including Dirac, Majorana, Dirac tachyon and Majorana tachyon. Constraints on Majorana wavefunctions limit the mass. Besides, there gives rise flatlands and Majorana particles hop in between, just mimicking the D-brane stack and open strings. Furthermore, a plausible way of ion-trapped experiment is suggeste…

This https://arxiv.org/abs/2305.06844 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Partial separability and symplectic-Haantjes manifolds
A theory of partial separability for classical Hamiltonian systems is proposed in the context of Haantjes geometry. As a general result, we show that the knowledge of a non-semisimple symplectic-Haantjes manifold for a given Hamiltonian system is sufficient to construct sets of coordinates (called Darboux-Haantjes coordinates) which allow both the partial separability of the associated Hamilton-Jacobi equations and the block-diagonalization of the operators of the corresponding Haantjes algeb…

Positive Steady-State Varieties of Small Chemical Reaction Networks
Maize Curiel, Elise Farr, Galileo Fries, Luis David Garc\'ia Puente, Julian Hutchins, Vuong Nguyen Hoang
https://arxiv.org/abs/2406.09514

Positive Steady-State Varieties of Small Chemical Reaction Networks
Chemical reaction network theory is a field of applied mathematics concerned with modeling chemical systems, and can be used in other contexts such as in systems biology to study cellular signaling pathways or epidemiology to study the effect of human interaction on the spread of disease. In this paper, we seek to understand a chemical reaction network's equilibrium points through the lens of algebraic geometry by computing the positive part of the steady-state variety defined by polynomial equ…

Stability of persistent currents in superfluid fermionic rings
Klejdja Xhani, Andrea Barresi, Marek Tylutki, Gabriel Wlaz{\l}owski, Piotr Magierski
https://arxiv.org/abs/2406.10088

Stability of persistent currents in superfluid fermionic rings
We investigate the stability of persistent currents in superfluid fermionic gases confined to a ring geometry. Our studies, conducted at zero temperature using time-dependent density functional theory, cover interaction regimes from strong (unitary Fermi gas) to weak (Bardeen-Cooper-Schrieffer regime) couplings. Stability is tested with respect to the presence of an external defect within the ring. The dissipation mechanism related to vortex generation is present in all interaction regimes. Int…

This https://arxiv.org/abs/2404.16097 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

K-theoretic Global Symmetry in String-constructed QFT and T-duality
We propose that generalized symmetries in some string-constructed QFTs are given by twisted K-theory, so as to be manifestly compatible with T-duality. We thus have even-form and odd-form symmetries determined by $K^*_N(\partial X)$, the twisted K-theory as D-brane charges on the asymptotic boundary $\partial X$ of internal geometry $X$ with twist class $N$. For these QFTs, "$p$-form symmetries" are no longer separately well-defined for individual $p$, but instead mixed up. We discuss 6D ADE-ty…

Minimal Submanifolds of the Classical Compact Riemannian Symmetric Spaces
Johanna Marie Gegenfurtner
https://arxiv.org/abs/2406.11294 https://arxiv.org/pdf/2406.11294
arXiv:2406.11294v1 Announce Type: new
Abstract: Minimal submanifolds constitute a central area within the realm of differential geometry, due to their many applications in various branches of physics. In this thesis we will employ a recent result of S. Gudmundsson and T.J. Munn to construct minimal submanifolds of the classical compact Riemannian symmetric spaces using eigenfunctions.

This https://arxiv.org/abs/2312.01486 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Elementary fractal geometry. 4. Automata-generated topological spaces
Finite automata were used to determine multiple addresses in number systems and to find topological properties of self-affine tiles and finite type fractals. We join these two lines of research by axiomatically defining automata which generate topological spaces. Simple examples show the potential of the concept. Spaces generated by automata are topologically self-similar. Two basic algorithms are outlined. The first one determines automata for all $k$-tuples of equivalent addresses from the au…

A splitting theorem for manifolds with a convex boundary component
Alessandro Cucinotta, Andrea Mondino
https://arxiv.org/abs/2406.09784 https://

A splitting theorem for manifolds with a convex boundary component
We prove a warped product splitting theorem for manifolds with Ricci curvature bounded from below in the spirit of [Croke-Kleiner, \emph{Duke Math.\;J}.\;(1992)], but instead of asking that one boundary component is compact and mean convex, we require that it is parabolic and convex. The parabolicity assumption cannot be dropped as, otherwise, the catenoid in ambient dimension four would give a counterexample. The result is an application of recently developed tools in synthetic geometry.

This https://arxiv.org/abs/2312.01486 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Elementary fractal geometry. 4. Automata-generated topological spaces
Finite automata were used to determine multiple addresses in number systems and to find topological properties of self-affine tiles and finite type fractals. We join these two lines of research by axiomatically defining automata which generate topological spaces. Simple examples show the potential of the concept. Spaces generated by automata are topologically self-similar. Two basic algorithms are outlined. The first one determines automata for all $k$-tuples of equivalent addresses from the au…

[2024-06-17 Mon (UTC), 2 new articles found for math.MG Metric Geometry]

[2024-06-17 Mon (UTC), 2 new articles found for math.MG Metric Geometry]