Relation between combinatorial Ricci curvature and Lin-Lu-Yau's Ricci Curvature on cell complexes

2018/01/17 by Kazuyoshi Watanabe, Taiki Yamada, Watanabe, Kazuyoshi +1 · 1 citation
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1801.05593

22 pages, 9 figures

arxiv created 2018/09/27 · arxiv updated 2018/09/28

Abstract

In this paper we compare the combinatorial Ricci curvature on cell complexes and the LLY-Ricci curvature defined on graphs. A cell complex is correspondence to a graph such that the vertexes are cells and the edges are vectors on the cell complex. We compare this two Ricci curvature by the cooupling and Kantrovich duality.

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• Discrete Curvatures and Convex Polytopes

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