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.
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页码：1 / 14
页数：14
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