arXiv math.MG Metric Geometry (@mathMGb) / X

arXiv math.MG Metric Geometry

14K posts

arXiv math.MG Metric Geometry

@mathMGb

Unofficial bot by @vela with github.com/so-okada/twXiv. @mathFAbot @mathGMb @mathGNb @mathGRbot @mathGTb @mathHOb @mathITbot @mathKTb @mathLOb @mathMPb ...

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Joined April 2013

arXiv math.MG Metric Geometry
@mathMGb
Dec 2, 2024
Jineon Baek: Optimality of Gerver's Sofa arxiv.org/abs/2411.19826 arxiv.org/pdf/2411.19826
arxiv.org
Optimality of Gerver's Sofa
We resolve the moving sofa problem by showing that Gerver's construction with 18 curve sections attains the maximum area $2.2195\cdots$.
670K
arXiv math.MG Metric Geometry
@mathMGb
Dec 20, 2024
Boaz Klartag, Joseph Lehec: Affirmative Resolution of Bourgain's Slicing Problem using Guan's Bound arxiv.org/abs/2412.15044 arxiv.org/pdf/2412.15044
5.5K
arXiv math.MG Metric Geometry
@mathMGb
Feb 18, 2025
Nakajima, Yamauchi, Zava: Topological dimension of the Gromov-Hausdorff and Gromov-Prokh... arxiv.org/abs/2502.11615 arxiv.org/pdf/2502.11615 arxiv.org/html/2502.11615
arxiv.org
Topological dimension of the Gromov-Hausdorff and Gromov-Prokhorov spaces
The Gromov-Hausdorff distance is a dissimilarity metric capturing how far two spaces are from being isometric. The Gromov-Prokhorov distance is a similar notion for metric measure spaces. In this...
571
arXiv math.MG Metric Geometry
@mathMGb
May 1, 2024
Ryoichiro Noda: Metrization of Gromov-Hausdorff-type topologies on boundedly-compact metric spaces arxiv.org/abs/2404.19681 arxiv.org/pdf/2404.19681
12K
arXiv math.MG Metric Geometry
@mathMGb
Aug 25, 2020
Yoshito Ishiki: An Embedding, An Extension, and An Interpolation of Ultrametrics arxiv.org/abs/2008.10209 arxiv.org/pdf/2008.10209
arXiv math.MG Metric Geometry
@mathMGb
Apr 17, 2023
Daisuke Kazukawa, Hiroki Nakajima, Takashi Shioya: Principal bundle structure of the space of metric measure spaces arxiv.org/abs/2304.06880 arxiv.org/pdf/2304.06880
arxiv.org
Principal bundle structure of the space of metric measure spaces
We study the topological structure of the space $\mathcal{X}$ of isomorphism classes of metric measure spaces equipped with the box or concentration topologies. We consider the scale-change action...
547
arXiv math.MG Metric Geometry
@mathMGb
Feb 23, 2024
Syota Esaki, Daisuke Kazukawa, Ayato Mitsuishi: Convergence of cones of metric measure spaces and its application to Cauchy distribution arxiv.org/abs/2402.14331 arxiv.org/pdf/2402.14331
arxiv.org
Convergence of cones of metric measure spaces and its application...
We prove that the sequence of cones of metric measure spaces converges if the sequence of base spaces converges in Gromov's box, concentration, and weak topologies. As an application, we show that...
259
arXiv math.MG Metric Geometry
@mathMGb
Jan 7, 2025
Shay Moran, Alexander Shlimovich, Amir Yehudayoff: Intuitive norms are Euclidean arxiv.org/abs/2501.02561 arxiv.org/pdf/2501.02561
240
arXiv math.MG Metric Geometry
@mathMGb
Mar 31, 2020
Yoshito Ishiki : An interpolation of metrics and spaces of metrics arxiv.org/abs/2003.13227 arxiv.org/pdf/2003.13227
arXiv math.MG Metric Geometry
@mathMGb
Dec 23, 2021
Goulnara Arzhantseva, Dawid Kielak, Tim de Laat, Damian Sawicki: Origami expanders arxiv.org/abs/2112.11864 arxiv.org/pdf/2112.11864
arxiv.org
Spectral gap and origami expanders
We construct the first measure-preserving affine actions with spectral gap on surfaces of arbitrary genus $g > 1$. We achieve this by finding geometric representatives of multi-twists on origami...
arXiv math.MG Metric Geometry
@mathMGb
Mar 6, 2020
Hajime Fujita, Yu Kitabeppu, Ayato Mitsuishi : Distance functions on convex bodies and symplectic toric manifolds arxiv.org/abs/2003.02293 arxiv.org/pdf/2003.02293
arxiv.org
Distance functions on convex bodies and symplectic toric manifolds
In this paper we discuss three distance functions on the set of convex bodies. In particular we study the convergence of Delzant polytopes, which are fundamental objects in symplectic toric...
arXiv math.MG Metric Geometry
@mathMGb
Jan 16, 2025
Hirokazu Katsumasa, Emily Roff, Masahiko Yoshinaga: Is magnitude 'generically continuous' for finite metric spaces? arxiv.org/abs/2501.08745 arxiv.org/pdf/2501.08745 arxiv.org/html/2501.08745
arxiv.org
Is magnitude 'generically continuous' for finite metric spaces?
Magnitude is a real-valued invariant of metric spaces which, in the finite setting, can be understood as recording the 'effective number of points' in a space as the scale of the metric varies....
6.3K
arXiv math.MG Metric Geometry
@mathMGb
Apr 16, 2024
Xinze Li: Lecture Notes on Comparison Geometry arxiv.org/abs/2404.09792 arxiv.org/pdf/2404.09792
arxiv.org
Lecture Notes on Comparison Geometry
This note is based on Professor Vitali Kapovitch's comparison geometry course at the University of Toronto. It delves into various comparison theorems, including those by Rauch and Toponogov,...
189
arXiv math.MG Metric Geometry
@mathMGb
Oct 24, 2017
Yoshito Ishiki : Quasi-symmetric invariant properties of Cantor metric spaces arxiv.org/abs/1710.08190