Long-Scale Ollivier Ricci Curvature of Graphs

IF 0.9 3区数学 Q2 MATHEMATICS Analysis and Geometry in Metric Spaces Pub Date : 2018-01-30 DOI:10.1515/agms-2019-0003

D. Cushing, S. Kamtue

引用次数: 8

Abstract

Abstract We study the long-scale Ollivier Ricci curvature of graphs as a function of the chosen idleness. Similarly to the previous work on the short-scale case, we show that this idleness function is concave and piecewise linear with at most 3 linear parts. We provide bounds on the length of the first and last linear pieces. We also study the long-scale curvature for the Cartesian product of two regular graphs.

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图的长尺度Ollivier Ricci曲率

研究了图的长尺度奥利维耶·里奇曲率作为所选空闲量的函数。与之前在短尺度情况下的工作类似，我们证明了该空闲函数是凹的，分段线性的，最多有3个线性部分。我们给出了第一个和最后一个线性片段的长度界限。我们还研究了两个正则图的笛卡尔积的长尺度曲率。

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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来源期刊

Analysis and Geometry in Metric Spaces Mathematics-Geometry and Topology

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

16 weeks

期刊介绍： Analysis and Geometry in Metric Spaces is an open access electronic journal that publishes cutting-edge research on analytical and geometrical problems in metric spaces and applications. We strive to present a forum where all aspects of these problems can be discussed. AGMS is devoted to the publication of results on these and related topics: Geometric inequalities in metric spaces, Geometric measure theory and variational problems in metric spaces, Analytic and geometric problems in metric measure spaces, probability spaces, and manifolds with density, Analytic and geometric problems in sub-riemannian manifolds, Carnot groups, and pseudo-hermitian manifolds. Geometric control theory, Curvature in metric and length spaces, Geometric group theory, Harmonic Analysis. Potential theory, Mass transportation problems, Quasiconformal and quasiregular mappings. Quasiconformal geometry, PDEs associated to analytic and geometric problems in metric spaces.

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