Curvature calculations for antitrees
Combinatorics
2018-01-30 v1
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-\'Emery 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.
Cite
@article{arxiv.1801.09400,
title = {Curvature calculations for antitrees},
author = {David Cushing and Shiping Liu and Florentin Münch and Norbert Peyerimhoff},
journal= {arXiv preprint arXiv:1801.09400},
year = {2018}
}