Curvature Calculations for Antitrees

Cushing, David; Liu, Shiping; Muench, Florentin; Peyerimhoff, Norbert

Abstract

In this article we prove that antitrees with suitable growth properties are examples of infinite graphs exhibiting strictly positive curvature in various contexts: in the normalized and non-normalized Bakry-Émery setting as well in the Ollivier-Ricci curvature case. We also show that these graphs do not have global positive lower curvature bounds, which one would expect in view of discrete analogues of the Bonnet-Myers theorem. The proofs in the different settings require different techniques.

Citation

Cushing, D., Liu, S., Muench, F., & Peyerimhoff, N. (2020). Curvature Calculations for Antitrees. In M. Keller, D. Lenz, & R. K. Wojciechowski (Eds.), Analysis and geometry on graphs and manifolds (21-54). Cambridge University Press. https://doi.org/10.1017/9781108615259.003

• Online Publication Date: Aug 1, 2020
• Publication Date: 2020-08
• Deposit Date: Jul 23, 2020
• Publicly Available Date: Feb 1, 2021
• Publisher: Cambridge University Press
• Pages: 21-54
• Series Title: London Mathematical Society Lecture Note Series
• Series Number: 461
• Book Title: Analysis and geometry on graphs and manifolds.
• ISBN: 9781108713184
• DOI: https://doi.org/10.1017/9781108615259.003
• Public URL: https://durham-repository.worktribe.com/output/1628091