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June 2020 Relation between Combinatorial Ricci Curvature and Lin-Lu-Yau's Ricci Curvature on Cell Complexes
Kazuyoshi WATANABE, Taiki YAMADA
Tokyo J. Math. 43(1): 25-45 (June 2020). DOI: 10.3836/tjm/1502179293

Abstract

In this paper we compare the combinatorial Ricci curvature on cell complexes and Lin-Lu-Yau's Ricci curvature defined on graphs. On a cell complex, the combinatorial Ricci curvature is introduced by the Bochner-Weitzenb\"{o}ck formula. A cell complex corresponds to a graph such that the vertices are cells and the edges are vectors on the cell complex. We compare these two kinds of Ricci curvatures by the coupling and the Kantorovich duality.

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Kazuyoshi WATANABE. Taiki YAMADA. "Relation between Combinatorial Ricci Curvature and Lin-Lu-Yau's Ricci Curvature on Cell Complexes." Tokyo J. Math. 43 (1) 25 - 45, June 2020. https://doi.org/10.3836/tjm/1502179293

Information

Published: June 2020
First available in Project Euclid: 8 March 2019

zbMATH: 07227180
MathSciNet: MR4121788
Digital Object Identifier: 10.3836/tjm/1502179293

Subjects:
Primary: 05E45
Secondary: 53B21

Rights: Copyright © 2020 Publication Committee for the Tokyo Journal of Mathematics

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Vol.43 • No. 1 • June 2020
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