Metric Geometry

Authors and titles for March 2025

[1] arXiv:2503.00021 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: New properties of length-extremals in free step-2 rank-4 Carnot groups Show Chinese title

Title: 自由步-2 秩-4 Carnot 群中长度极值的新性质

Annamaria Montanari, Daniele Morbidelli

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

[2] arXiv:2503.00153 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: On $L_p$ Brunn-Minkowski type inequalities for a general class of functionals Show Chinese title

Title: 关于一般函数类的$L_p$型Brunn-Minkowski不等式

Lidia Gordo Malagón, Jesús Yepes Nicolás

Comments: Improved presentation. Corrected typos. Main results unchanged

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

[3] arXiv:2503.00212 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Flat grazes of convex bodies and local characterization of quadrics Show Chinese title

Title: 凸体的平坦区域和二次曲面的局部特征 characterization

Jesús Jerónimo-Castro, Luis Montejano, Efrén Morales-Amaya

Subjects: Metric Geometry (math.MG)

[4] arXiv:2503.00949 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: On general versions of the Petty projection inequality Show Chinese title

Title: 关于佩蒂投影不等式的普遍形式

Francisco Marín Sola

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

[5] arXiv:2503.00970 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: The $L_{p}$ Gaussian Minkowski problem for $C$-pseudo-cones Show Chinese title

Title: $L_{p}$ 高斯闵可夫斯基问题对于$C$-伪圆锥

Junjie Shan, Wenchuan Hu

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

[6] arXiv:2503.02599 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Isometries of the class of ball-bodies Show Chinese title

Title: 球体的等距变换

Shiri Artstein-Avidan, Arnon Chor, Dan Florentin

Comments: Final version

Subjects: Metric Geometry (math.MG)

[7] arXiv:2503.02613 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: A full classification of the isometries of the class of ball-bodies Show Chinese title

Title: 球体类的等距映射的完全分类

Shiri Artstein-Avidan, Arnon Chor, Dan Florentin

Subjects: Metric Geometry (math.MG)

[8] arXiv:2503.03442 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: On the uniform convexity of the squared distance Show Chinese title

Title: 关于平方距离的一致凸性

Andrei Sipos

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

[9] arXiv:2503.05392 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: New fiber and graph combinations of convex bodies Show Chinese title

Title: 凸体的新纤维和图组合

Steven Hoehner, Sudan Xing

Comments: 35 pages, 3 figures

Subjects: Metric Geometry (math.MG)

[10] arXiv:2503.05435 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: The excenters of bicentric polygons are concyclic Show Chinese title

Title: 圆外切多边形的旁心共圆

Norbert Hungerbühler, Clemens Pohle, Yun Zhang

Comments: 12 pages, 10 figures

Subjects: Metric Geometry (math.MG)

[11] arXiv:2503.05901 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: On computable classes of equidistant sets: multivariate equidistant functions Show Chinese title

Title: 可计算的等距集类：多元等距函数

Ábris Nagy, Márk Oláh, Myroslav Stoika, Csaba Vincze

Comments: 14 pages, 3 figures

Subjects: Metric Geometry (math.MG)

[12] arXiv:2503.06191 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: On the polar of Schneider's difference body Show Chinese title

Title: 论施耐德差体的极

Julián Haddad, Dylan Langharst, Galyna V. Livshyts, Eli Putterman

Comments: 31 pages, comments welcome. Updated presentation of some facts. Keywords: Schneider's conjecture, Blaschke-Santal\'o inequality, polarity

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

[13] arXiv:2503.07287 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: A Klain-Schneider Theorem for Vector-Valued Valuations on Convex Functions Show Chinese title

Title: 向量值赋值在凸函数上的Klain-Schneider定理

Mohamed A. Mouamine, Fabian Mussnig

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

[14] arXiv:2503.09253 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Smooth Approximations of Quasispheres Show Chinese title

Title: 光滑逼近的拟球面

Spencer Cattalani

Comments: 8 pages; improved exposition

Subjects: Metric Geometry (math.MG) ; Complex Variables (math.CV)

[15] arXiv:2503.09284 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Gromov-Hausdorff convergence of maximal Gromov hyperbolic spaces and their boundaries Show Chinese title

Title: 极大Gromov双曲空间及其边界的Gromov-Hausdorff收敛性

Kingshook Biswas, Arkajit Pal Choudhury

Comments: 38 pages. Introduction rewritten, added Corollary 1.2

Subjects: Metric Geometry (math.MG)

[16] arXiv:2503.09542 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: A note on Erdős matrices and Marcus\unicode{x2013}Ree inequality Show Chinese title

Title: 关于Erdős矩阵和Marcus\unicode{x2013}Ree不等式的一篇注记

Aman Kushwaha, Raghavendra Tripathi

Comments: 20 pages + appendix (2 pages); 3 tables; Minor changes to improve readability and correction of typos; This is the accepted version in Linear Algebra and its Applications

Journal-ref: Linear Algebra and its Applications 725 (2025), p. 223-247

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

[17] arXiv:2503.09582 (cross-list from math.MG) [cn-pdf, pdf, other]

Title: Exotic spherical flexible octahedra and counterexamples to the Modified Bellows Conjecture Show Chinese title

Title: 奇特球面柔体八面体和对修改后的Bellows猜想的反例

Alexander A. Gaifullin

Comments: 21 pages

Subjects: Metric Geometry (math.MG)

[18] arXiv:2503.10376 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Quasigeodesics on the Cube Show Chinese title

Title: 立方体上的拟测地线

MIT CompGeom Group, Hugo A. Akitaya, Erik D. Demaine, Adam Hesterberg, Thomas C. Hull, Anna Lubiw, Jayson Lynch, Klara Mundilova, Chie Nara, Joseph O'Rourke, Frederick Stock, Josef Tkadlec, Ryuhei Uehara

Comments: 15 pages, 11 figures, 13 references

Subjects: Metric Geometry (math.MG)

[19] arXiv:2503.10449 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Measure transport via pseudo-cones Show Chinese title

Title: 通过伪锥的测度传输

Rolf Schneider

Comments: 8 pages

Subjects: Metric Geometry (math.MG)

[20] arXiv:2503.12939 (cross-list from math.MG) [cn-pdf, pdf, other]

Title: The infimal convolution structure of the Hellinger-Kantorovich distance Show Chinese title

Title: Hellinger-Kantorovich距离的最小卷积结构

Nicolò De Ponti, Giacomo Enrico Sodini, Luca Tamanini

Comments: 53 pages

Subjects: Metric Geometry (math.MG) ; Functional Analysis (math.FA) ; Optimization and Control (math.OC) ; Probability (math.PR)

[21] arXiv:2503.13258 (cross-list from math.MG) [cn-pdf, pdf, other]

Title: Construction of self-similar energy forms and singularity of Sobolev spaces on Laakso-type fractal spaces Show Chinese title

Title: 自相似能量形式的构造与Laakso型分形空间上Sobolev空间的奇异性

Riku Anttila, Sylvester Eriksson-Bique, Ryosuke Shimizu

Comments: 80 Pages, comments are welcome!

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

[22] arXiv:2503.14132 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: A note on Laplacian bounds, deformation properties and isoperimetric sets in metric measure spaces Show Chinese title

Title: 关于拉普拉斯界、变形性质和度量测度空间中的等周集的注记

Enrico Pasqualetto, Tapio Rajala

Comments: 20 pages

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

[23] arXiv:2503.14548 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: A very short proof of the Figiel-Lindenstrauss-Milman theorem Show Chinese title

Title: Figiel-Lindenstrauss-Milman定理的一个非常短的证明

Tomer Milo

Comments: 2 pages

Subjects: Metric Geometry (math.MG)

[24] arXiv:2503.15159 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Characterising 1-rectifiable metric spaces via connected tangent spaces Show Chinese title

Title: 具有连通切空间的度量空间的1-可微分特征

David Bate, Phoebe Valentine

Subjects: Metric Geometry (math.MG)

[25] arXiv:2503.15716 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Closed BV-extension and $W^{1,1}$-extension sets Show Chinese title

Title: 闭的BV扩张和$W^{1,1}$-扩张集

Emanuele Caputo, Jesse Koivu, Danka Lučić, Tapio Rajala

Comments: 42 pages, 2 figures

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

[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)