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Curvature Calculations for Antitrees

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

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David Cushing

Shiping Liu

Florentin Muench


Matthias Keller

Daniel Lenz

Radoslaw K. Wojciechowski


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.


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.

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


Published Book Chapter (1.2 Mb)

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.

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