Metric Geometry

Authors and titles for March 2025

[26] arXiv:2503.18157 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: The superposition principle for local 1-dimensional currents Show Chinese title

Title: 局部一维电流的叠加原理

Luigi Ambrosio, Federico Renzi, Federico Vitillaro

Subjects: Metric Geometry (math.MG) ; Analysis of PDEs (math.AP) ; Functional Analysis (math.FA)

[27] arXiv:2503.18343 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Horoboundaries of coarsely convex spaces Show Chinese title

Title: 粗凸空间的Horoboundary

Ikkei Sato

Comments: 32 pages

Subjects: Metric Geometry (math.MG)

[28] arXiv:2503.18779 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Asymptotics of the quantization problem on metric measure spaces Show Chinese title

Title: 度量测度空间上量化问题的渐近性

Ata Deniz Aydin

Comments: 32 pages + 17 page appendix

Subjects: Metric Geometry (math.MG) ; Analysis of PDEs (math.AP) ; Optimization and Control (math.OC)

[29] arXiv:2503.19528 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Moments of the Cramér transform of log-concave probability measures Show Chinese title

Title: 对数凹概率测度的Cramér变换矩

Apostolos Giannopoulos, Natalia Tziotziou

Comments: 24 pages

Subjects: Metric Geometry (math.MG) ; Functional Analysis (math.FA) ; Probability (math.PR)

[30] arXiv:2503.19729 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Roots of real-valued zero mean maps: Compositions of linear functionals and equivariant maps Show Chinese title

Title: 实值零均值映射的根：线性泛函和等变映射的复合

Francesca Cantor, Julia D'Amico, Florian Frick, Eric Myzelev

Comments: 17 pages

Subjects: Metric Geometry (math.MG) ; Classical Analysis and ODEs (math.CA)

[31] arXiv:2503.20458 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Amicable Triangle and Rectangles on the Integer Lattice Show Chinese title

Title: 友爱三角形和整数格上的矩形

Iwan Praton, Weiran Zeng

Subjects: Metric Geometry (math.MG) ; Combinatorics (math.CO)

[32] arXiv:2503.21478 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Equilateral dimension of the planar Banach--Mazur compactum Show Chinese title

Title: 平面Banach--Mazur紧集的等边维数

Tomasz Kobos, Konrad Swanepoel

Subjects: Metric Geometry (math.MG) ; Functional Analysis (math.FA)

[33] arXiv:2503.21494 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Inequalities for sections and projections of log-concave functions Show Chinese title

Title: 对数凹函数的截面和投影的不等式

Natalia Tziotziou

Comments: 24 pages

Subjects: Metric Geometry (math.MG)

[34] arXiv:2503.22671 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Non-Archimedean Hilbert geometry and degenerations of real Hilbert geometries Show Chinese title

Title: 非阿基米德希尔伯特几何与实希尔伯特几何的退化

Xenia Flamm, Anne Parreau

Comments: 44 pages, 13 figures, comments welcome!

Subjects: Metric Geometry (math.MG) ; Differential Geometry (math.DG) ; Geometric Topology (math.GT)

[35] arXiv:2503.22680 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: On the number of defects in optimal quantizers on closed surfaces: the hexagonal torus Show Chinese title

Title: 闭曲面上最优量化器的缺陷数量：六边形环面

Jack Edward Tisdell, Rustum Choksi, Xin Yang Lu

Comments: 26 pages, 6 figures; corrected typos

Subjects: Metric Geometry (math.MG) ; Optimization and Control (math.OC)

[36] arXiv:2503.22895 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Critical modular lattices in the Gaussian core model Show Chinese title

Title: 高斯核心模型中的临界模格

Arian Joharian, Frank Vallentin, Marc Christian Zimmermannn

Comments: 31 pages

Subjects: Metric Geometry (math.MG) ; Number Theory (math.NT)

[37] arXiv:2503.23423 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Construction of graph-directed invariant sets of weak contractions on semi-metric spaces Show Chinese title

Title: 弱压缩映射在半度量空间上的图导向不变集的构造

Kazuki Okamura

Comments: v2: minor revision; 21 pages, 4 figures; to appear in Aequationes Mathematicae

Subjects: Metric Geometry (math.MG) ; Classical Analysis and ODEs (math.CA) ; Functional Analysis (math.FA)

[38] arXiv:2503.24161 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Hypergenerated Carnot groups Show Chinese title

Title: 超生成的Carnot群

Enrico Le Donne, Luca Nalon, Nicola Paddeu, Simone Verzellesi

Comments: 22 pages

Subjects: Metric Geometry (math.MG) ; Differential Geometry (math.DG) ; Group Theory (math.GR)

[39] arXiv:2503.00560 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Asymptotics of Riemannian Lie groups with nilpotency step 2 Show Chinese title

Title: 二步幂零黎曼李群的渐进行为

Enrico Le Donne, Luca Nalon, Sebastiano Nicolussi Golo, Seung-Yeon Ryoo

Subjects: Differential Geometry (math.DG) ; Group Theory (math.GR) ; Metric Geometry (math.MG)

[40] arXiv:2503.01373 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Tangency sets of non-involutive distributions and unrectifiability in Carnot-Carathéodory spaces Show Chinese title

Title: 非齐次分布的切触集与Carnot-Carathéodory空间中的不可直化性

Giovanni Alberti, Annalisa Massaccesi, Andrea Merlo

Subjects: Differential Geometry (math.DG) ; Functional Analysis (math.FA) ; Metric Geometry (math.MG)

[41] arXiv:2503.01664 (cross-list from cs.LG) [cn-pdf, pdf, html, other]

Title: Merging Hazy Sets with m-Schemes: A Geometric Approach to Data Visualization Show Chinese title

Title: 模糊集与m方案的融合：数据可视化的一种几何方法

Lukas Silvester Barth, Hannaneh Fahimi, Parvaneh Joharinad, Jürgen Jost, Janis Keck

Subjects: Machine Learning (cs.LG) ; Discrete Mathematics (cs.DM) ; Metric Geometry (math.MG)

[42] arXiv:2503.01911 (cross-list from math.CO) [cn-pdf, pdf, html, other]

Title: Planar lattices and equilateral odd-gons Show Chinese title

Title: 平面格点和等边奇数边形

Akira Iino, Masashi Sakiyama

Comments: 7 pages, to appear in Yokohama Mathematical Journal

Journal-ref: Yokohama Math. J. 70 (2024) 235-242

Subjects: Combinatorics (math.CO) ; Metric Geometry (math.MG) ; Number Theory (math.NT)

[43] arXiv:2503.01988 (cross-list from cs.CG) [cn-pdf, pdf, html, other]

Title: Software for the Thompson and Funk Polygonal Geometry Show Chinese title

Title: 用于汤普森和弗unk多边形几何的软件

Hridhaan Banerjee, Carmen Isabel Day, Auguste H. Gezalyan, Olga Golovatskaia, Megan Hunleth, Sarah Hwang, Nithin Parepally, Lucy Wang, David M. Mount

Subjects: Computational Geometry (cs.CG) ; Metric Geometry (math.MG)

[44] arXiv:2503.02596 (cross-list from math.FA) [cn-pdf, pdf, html, other]

Title: Derivations and Sobolev functions on extended metric-measure spaces Show Chinese title

Title: 导数和扩展度量测度空间上的Sobolev函数

Enrico Pasqualetto, Janne Taipalus

Comments: 43 pages

Subjects: Functional Analysis (math.FA) ; Analysis of PDEs (math.AP) ; Metric Geometry (math.MG)

[45] arXiv:2503.04285 (cross-list from math.FA) [cn-pdf, pdf, html, other]

Title: SBV functions in Carnot-Carathéodory spaces Show Chinese title

Title: SBV 函数在 Carnot-Carathéodory 空间中

Marco Di Marco, Sebastiano Don, Davide Vittone

Comments: 26 pages

Subjects: Functional Analysis (math.FA) ; Classical Analysis and ODEs (math.CA) ; Metric Geometry (math.MG)

[46] arXiv:2503.05521 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Warped products and synthetic lower curvature bounds: an overview Show Chinese title

Title: 扭曲乘积和合成下界曲率：概述

Christian Ketterer

Comments: revised introduction with additional references; 26 page, comments are welcome, this is a survey article

Subjects: Differential Geometry (math.DG) ; Metric Geometry (math.MG)

[47] arXiv:2503.06180 (cross-list from math.PR) [cn-pdf, pdf, html, other]

Title: Multiplicative convolution with symmetries in Euclidean space and on the sphere Show Chinese title

Title: 欧几里得空间和球面上具有对称性的乘法卷积

Felix Nagel

Comments: 57 pages

Subjects: Probability (math.PR) ; Functional Analysis (math.FA) ; Metric Geometry (math.MG)

[48] arXiv:2503.06673 (cross-list from math.GR) [cn-pdf, pdf, html, other]

Title: On boundaries of bicombable spaces Show Chinese title

Title: 关于双可组合空间的边界

Daniel Danielski

Comments: Modifications in the Introduction and Remark 2.5 regarding the [Bas24] paper. Section 5 adapted to work under more general assumptions, in view of the [HHP25] paper

Subjects: Group Theory (math.GR) ; Metric Geometry (math.MG)

[49] arXiv:2503.06799 (cross-list from math.DS) [cn-pdf, pdf, html, other]

Title: Local inverse measure-theoretic entropy for endomorphisms Show Chinese title

Title: 局部逆测度论熵对于自映射

Eugen Mihailescu, Radu B. Munteanu

Subjects: Dynamical Systems (math.DS) ; Metric Geometry (math.MG) ; Probability (math.PR)

[50] arXiv:2503.07228 (cross-list from math.CO) [cn-pdf, pdf, html, other]

Title: Counting for rigidity under projective transformations in the plane Show Chinese title

Title: 平面射影变换下的刚性计数

Leah Wrenn Berman, Signe Lundqvist, Bernd Schulze, Brigitte Servatius, Herman Servatius, Klara Stokes, Walter Whiteley

Comments: 21 pages, 20 figures

Subjects: Combinatorics (math.CO) ; Metric Geometry (math.MG)