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2 - Curvature Calculations for Antitrees

Published online by Cambridge University Press:  14 August 2020

Matthias Keller
Affiliation:
Universität Potsdam, Germany
Daniel Lenz
Affiliation:
Universität Potsdam, Germany
Radoslaw K. Wojciechowski
Affiliation:
York College of the City University of New York
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Summary

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.

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Publisher: Cambridge University Press
Print publication year: 2020

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