Communications in Analysis and Geometry

Volume 31 (2023)

Number 5

Maximal diameter theorem for directed graphs of positive Ricci curvature

Pages: 1275 – 1298

DOI: https://dx.doi.org/10.4310/CAG.2023.v31.n5.a7

Authors

Ryunosuke Ozawa (Department of Mathematics, National Defense Academy of Japan, Yokosuka, Japan)

Yohei Sakurai (Department of Mathematics, Saitama University, Japan)

Taiki Yamada (Department of Mathematics, Shimane University, Japan)

Abstract

In a previous work, the authors $\href{https://doi.org/10.1007/s00526-020-01809-2}{[15]}$ have introduced a Lin–Lu–Yau type Ricci curvature for directed graphs, and obtained a diameter comparison of Bonnet–Myers type. In this paper, we investigate rigidity properties for the equality case, and conclude a maximal diameter theorem of Cheng type.

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The first named author was supported in part by JSPS KAKENHI(19K14532). The first and second named authors were supported in partby JSPS Grant-in-Aid for Scientific Research on Innovative Areas “DiscreteGeometric Analysis for Materials Design” (17H06460). The third namedauthor was supported in part by JSPS KAKENHI (19K23411).

Received 14 December 2020

Accepted 22 April 2021

Published 16 July 2024