Distance Bounds for Graphs with Some Negative Bakry-Emery Curvature

被引：10

作者：

Liu, Shiping ^{[1
]}

Muench, Florentin ^{[2
]}

Peyerimhoff, Norbert ^{[3
]}

Rose, Christian ^{[2
]}

机构：

[1] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China

[2] Max Planck Inst Math Nat Wissensch, Inselstr 22, D-04103 Leipzig, Germany

[3] Univ Durham, Dept Math Sci, Durham DH1 3LE, England

来源：

ANALYSIS AND GEOMETRY IN METRIC SPACES | 2019年 / 7卷 / 01期

关键词：

Bakry-Emery curvature; discrete Bonnet-Myers theorem; intrinsic metric; heat semigroup; METRIC-MEASURE-SPACES; LI-YAU INEQUALITY; RICCI CURVATURE; STOCHASTIC COMPLETENESS; LAPLACIAN; SPECTRUM; GEOMETRY;

D O I：

10.1515/agms-2019-0001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove distance bounds for graphs possessing positive Bakry-Emery curvature apart from an exceptional set, where the curvature is allowed to be non-positive. If the set of non-positively curved vertices is finite, then the graph admits an explicit upper bound for the diameter. Otherwise, the graph is a subset of the tubular neighborhood with an explicit radius around the non-positively curved vertices. Those results seem to be the first assuming non-constant Bakry-Emery curvature assumptions on graphs.

引用

页码：1 / 14

页数：14

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