具有负Bakry-Émery曲率的图的距离界

Pub Date : 2017-05-23 DOI:10.1515/agms-2019-0001

Shiping Liu, Florentin Münch, N. Peyerimhoff, Christian Rose

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引用次数: 13

摘要

摘要我们证明了具有正Bakry-Émery曲率的图的距离界，除了一个例外集，其中曲率是非正的。如果非正弯曲顶点的集合是有限的，那么图允许直径的显式上界。否则，图是管状邻域的子集，在非正弯曲顶点周围具有显式半径。这些结果似乎是第一个假设图上的非常数Bakry-Émery曲率假设。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Distance Bounds for Graphs with Some Negative Bakry-Émery Curvature

Abstract We prove distance bounds for graphs possessing positive Bakry-Émery 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-Émery curvature assumptions on graphs.

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