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Curvature calculations for antitrees.

Cushing, David and Liu, Shiping and Muench, Florentin and Peyerimhoff, Norbert (2020) 'Curvature calculations for antitrees.', in Analysis and geometry on graphs and manifolds. Cambridge: Cambridge University Press, pp. 21-54. London Mathematical Society Lecture Note Series., 461

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.

Item Type:Book chapter
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1017/9781108615259.003
Publisher statement:This material has been published in Analysis and Geometry on Graphs and Manifolds edited by Matthias Keller, Daniel Lenz and Radoslaw K. Wojciechowski. This version is free to view and download for personal use only. Not for re-distribution, re-sale or use in derivative works. © Cambridge University Press 2020.
Date accepted:No date available
Date deposited:23 July 2020
Date of first online publication:01 August 2020
Date first made open access:01 February 2021

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