Geometric and spectral properties of directed graphs under a lower Ricci curvature bound

被引：5

作者：

Ozawa, Ryunosuke ^{[1
]}

Sakurai, Yohei ^{[1
]}

Yamada, Taiki ^{[2
]}

机构：

[1] Tohoku Univ, Adv Inst Mat Res AIMR, Aoba Ku, 2-1-1 Katahira, Sendai, Miyagi 9808577, Japan

[2] Res Inst Humanity & Nat, Kita Ku, 457-4 Motoyama, Kyoto 6038047, Japan

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2020年 / 59卷 / 04期

关键词：

Primary; 05C20; 05C12; 05C81; 53C21; 53C23; ISOPERIMETRIC-INEQUALITIES; CHEEGER-INEQUALITY; EIGENVALUES; LAPLACIANS; DIAMETER; THEOREM; VOLUME;

D O I：

10.1007/s00526-020-01809-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For undirected graphs, the Ricci curvature introduced by Lin-Lu-Yau has been widely studied from various perspectives, especially geometric analysis. In the present paper, we discuss generalization problem of their Ricci curvature for directed graphs. We introduce a new generalization for strongly connected directed graphs by using the mean transition probability kernel which appears in the formulation of the Chung Laplacian. We conclude several geometric and spectral properties under a lower Ricci curvature bound extending previous results in the undirected case.

引用

页数：39

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