Curvature Calculations for Antitrees

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

doi:10.1017/9781108615259.003

Curvature Calculations for Antitrees

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

Authors

David Cushing

Shiping Liu

Florentin Muench

Professor Norbert Peyerimhoff norbert.peyerimhoff@durham.ac.uk
Professor

Contributors

Matthias Keller
Editor

Daniel Lenz
Editor

Radoslaw K. Wojciechowski
Editor

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

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Copyright 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.