Rigidity properties of the hypercube via Bakry-emery curvature

被引：2
作者：
Liu, Shiping [1 ]
Muench, Florentin [2 ]
Peyerimhoff, Norbert [3 ]
机构：
[1] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China
[2] Max Planck Inst Math Sci Leipzig, D-04103 Leipzig, Germany
[3] Univ Durham, Dept Math Sci, Durham DH1 3LE, England
来源：
MATHEMATISCHE ANNALEN | 2024年 / 388卷 / 02期
基金：
英国工程与自然科学研究理事会; 中国国家自然科学基金;
关键词：
METRIC-MEASURE-SPACES; RICCI CURVATURE; INEQUALITIES;
D O I：
10.1007/s00208-022-02537-y
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We give rigidity results for the discrete Bonnet-Myers diameter bound and the Lichnerowicz eigenvalue estimate. Both inequalities are sharp if and only if the underlying graph is a hypercube. The proofs use well-known semigroup methods as well as new direct methods which translate curvature to combinatorial properties. Our results can be seen as first known discrete analogues of Cheng's and Obata's rigidity theorems.
引用
收藏
页码：1225 / 1259
页数：35
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