Skip to main content

Research Repository

Advanced Search

Bakry–Émery curvature and diameter bounds on graphs

Liu, Shiping; Münch, Florentin; Peyerimhoff, Norbert

Bakry–Émery curvature and diameter bounds on graphs Thumbnail


Authors

Shiping Liu

Florentin Münch



Abstract

We prove finiteness and diameter bounds for graphs having a positive Ricci-curvature bound in the Bakry–Émery sense. Our first result using only curvature and maximal vertex degree is sharp in the case of hypercubes. The second result depends on an additional dimension bound, but is independent of the vertex degree. In particular, the second result is the first Bonnet–Myers type theorem for unbounded graph Laplacians. Moreover, our results improve diameter bounds from Fathi and Shu (Bernoulli 24(1):672–698, 2018) and Horn et al. (J für die reine und angewandte Mathematik (Crelle’s J), 2017, https://doi.org/10.1515/crelle-2017-0038) and solve a conjecture from Cushing et al. (Bakry–Émery curvature functions of graphs, 2016).

Citation

Liu, S., Münch, F., & Peyerimhoff, N. (2018). Bakry–Émery curvature and diameter bounds on graphs. Calculus of Variations and Partial Differential Equations, 57(2), Article 67. https://doi.org/10.1007/s00526-018-1334-x

Journal Article Type Article
Acceptance Date Feb 28, 2018
Online Publication Date Mar 15, 2018
Publication Date Mar 15, 2018
Deposit Date May 1, 2018
Publicly Available Date Mar 15, 2019
Journal Calculus of Variations and Partial Differential Equations
Print ISSN 0944-2669
Electronic ISSN 1432-0835
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 57
Issue 2
Article Number 67
DOI https://doi.org/10.1007/s00526-018-1334-x

Files




You might also like



Downloadable Citations