A New Transport Distance and Its Associated Ricci Curvature of Hypergraphs

IF 0.9 3区数学 Q2 MATHEMATICS

Analysis and Geometry in Metric Spaces Pub Date : 2021-05-14 DOI:10.1515/agms-2022-0135

Tomoya Akamatsu

引用次数: 3

Abstract

Abstract The coarse Ricci curvature of graphs introduced by Ollivier as well as its modification by Lin–Lu– Yau have been studied from various aspects. In this paper, we propose a new transport distance appropriate for hypergraphs and study a generalization of Lin–Lu–Yau type curvature of hypergraphs. As an application, we derive a Bonnet–Myers type estimate for hypergraphs under a lower Ricci curvature bound associated with our transport distance. We remark that our transport distance is new even for graphs and worthy of further study.

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超图的一个新的输运距离及其关联Ricci曲率

摘要从多个方面研究了Ollivier引入的图的粗糙Ricci曲率以及Lin–Lu–Yau对其的修正。在本文中，我们提出了一个适用于超图的新的输运距离，并研究了超图的Lin–Lu–Yau型曲率的推广。作为一个应用，我们推导了超图在与传输距离相关的较低Ricci曲率界下的Bonnet–Myers型估计。我们注意到，即使对于图形来说，我们的运输距离也是新的，值得进一步研究。

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.