arXiv - MATH - Metric Geometry最新文献_第10页

On iterated circumcenter sequences 关于迭代圆心序列

arXiv - MATH - Metric Geometry Pub Date : 2024-07-29 DOI: arxiv-2407.19767

Shuho Kanda, Junnosuke Koizumi

引用次数: 0

Bi-Lipschitz embedding metric triangles in the plane 平面中的双唇边嵌入度量三角形

arXiv - MATH - Metric Geometry Pub Date : 2024-07-29 DOI: arxiv-2407.20019

Xinyuan Luo, Matthew Romney, Alexandria L. Tao

引用次数: 0

Uniform waist inequalities in codimension two for manifolds with Kazhdan fundamental group 具有卡兹丹基群流形的二维均匀腰不等式

arXiv - MATH - Metric Geometry Pub Date : 2024-07-29 DOI: arxiv-2407.19783

Uri Bader, Roman Sauer

引用次数: 0

The Weighted $L^p$ Minkowski Problem 加权$L^p$闵科夫斯基问题

arXiv - MATH - Metric Geometry Pub Date : 2024-07-29 DOI: arxiv-2407.20064

Dylan Langharst, Jiaqian Liu, Shengyu Tang

{"title":"The Weighted $L^p$ Minkowski Problem","authors":"Dylan Langharst, Jiaqian Liu, Shengyu Tang","doi":"arxiv-2407.20064","DOIUrl":"https://doi.org/arxiv-2407.20064","url":null,"abstract":"The Minkowski problem in convex geometry concerns showing a given Borel\u0000measure on the unit sphere is, up to perhaps a constant, some type of surface\u0000area measure of a convex body. Two types of Minkowski problems in particular\u0000are an active area of research: $L^p$ Minkowski problems, introduced by Lutwak\u0000and (Lutwak,Yang, and Zhang), and weighted Minkowski problems, introduced by\u0000Livshyts. For the latter, the Gaussian Minkowski problem, whose primary\u0000investigators were (Huang, Xi and Zhao), is the most prevalent. In this work,\u0000we consider weighted surface area in the $L^p$ setting. We propose a framework\u0000going beyond the Gaussian setting by focusing on rotational invariant measures,\u0000mirroring the recent development of the Gardner-Zvavitch inequality for\u0000rotational invariant, log-concave measures. Our results include existence for\u0000all $p in mathbb R$ (with symmetry assumptions in certain instances). We also\u0000have uniqueness for $p geq 1$ under a concavity assumption. Finally, we obtain\u0000results in the so-called $small$ $mass$ $regime$ using degree theory, as\u0000instigated in the Gaussian case by (Huang, Xi and Zhao). Most known results for\u0000the Gaussian Minkowski problem are then special cases of our main theorems.","PeriodicalId":501444,"journal":{"name":"arXiv - MATH - Metric Geometry","volume":"51 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141870124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Centroids and equilibrium points of convex bodies 凸体的中心点和平衡点

arXiv - MATH - Metric Geometry Pub Date : 2024-07-27 DOI: arxiv-2407.19177

Zsolt Lángi, Péter L. Várkonyi

引用次数: 0

Sigma-compactness of Morse boundaries in Morse local-to-global groups and applications to stationary measures 莫尔斯局部到全局群中莫尔斯边界的西格玛紧密性及其在静态量纲中的应用

arXiv - MATH - Metric Geometry Pub Date : 2024-07-26 DOI: arxiv-2407.18863

Vivian He, Davide Spriano, Stefanie Zbinden

引用次数: 0

Rigidity of proper quasi-homogeneous domains in positive flag manifolds 正旗流形中适当准均质域的刚性

arXiv - MATH - Metric Geometry Pub Date : 2024-07-26 DOI: arxiv-2407.18747

Blandine Galiay

引用次数: 0

Proper quasi-homogeneous domains of the Einstein universe 爱因斯坦宇宙的适当准均质域

arXiv - MATH - Metric Geometry Pub Date : 2024-07-26 DOI: arxiv-2407.18577

Adam ChalumeauIRMA, Blandine GaliayIHES

引用次数: 0

Borell's inequality and mean width of random polytopes via discrete inequalities 博雷尔不等式和通过离散不等式求随机多面体的平均宽度

arXiv - MATH - Metric Geometry Pub Date : 2024-07-25 DOI: arxiv-2407.18235

David Alonso-Gutiérrez, Luis C. García-Lirola

{"title":"Borell's inequality and mean width of random polytopes via discrete inequalities","authors":"David Alonso-Gutiérrez, Luis C. García-Lirola","doi":"arxiv-2407.18235","DOIUrl":"https://doi.org/arxiv-2407.18235","url":null,"abstract":"Borell's inequality states the existence of a positive absolute constant\u0000$C>0$ such that for every $1leq pleq q$ $$ left(mathbb E|langle X,\u0000e_nrangle|^pright)^frac{1}{p}leqleft(mathbb E|langle X,\u0000e_nrangle|^qright)^frac{1}{q}leq Cfrac{q}{p}left(mathbb E|langle X,\u0000e_nrangle|^pright)^frac{1}{p}, $$ whenever $X$ is a random vector uniformly\u0000distributed in any convex body $Ksubseteqmathbb R^n$ containing the origin in\u0000its interior and $(e_i)_{i=1}^n$ is the standard canonical basis in $mathbb\u0000R^n$. In this paper, we will prove a discrete version of this inequality, which\u0000will hold whenever $X$ is a random vector uniformly distributed on\u0000$Kcapmathbb Z^n$ for any convex body $Ksubseteqmathbb R^n$ containing the\u0000origin in its interior. We will also make use of such discrete version to\u0000obtain discrete inequalities from which we can recover the estimate $mathbb E\u0000w(K_N)sim w(Z_{log N}(K))$ for any convex body $K$ containing the origin in\u0000its interior, where $K_N$ is the centrally symmetric random polytope\u0000$K_N=operatorname{conv}{pm X_1,ldots,pm X_N}$ generated by independent\u0000random vectors uniformly distributed on $K$ and $w(cdot)$ denotes the mean\u0000width.","PeriodicalId":501444,"journal":{"name":"arXiv - MATH - Metric Geometry","volume":"47 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141785618","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On homogeneous Newton-Sobolev spaces of functions in metric measure spaces of uniformly locally controlled geometry 论均匀局部控制几何公度量空间中函数的同质牛顿-索博列夫空间

arXiv - MATH - Metric Geometry Pub Date : 2024-07-25 DOI: arxiv-2407.18315

Ryan Gibara, Ilmari Kangasniemi, Nageswari Shanmugalingam

引用次数: 0