Large scale Ricci curvature on graphs
Combinatorics
2019-06-17 v1 Differential Geometry
Abstract
We define a hybrid between Ollvier and Bakry Emery curvature on graphs with dependence on a variable neighborhood. The hexagonal lattice is non-negatively curved under this new curvature notion. Bonnet-Myers diameter bounds and Lichnerowicz eigenvalue estimates follow from the standard arguments. We prove gradient estimates similar to the ones obtained from Bakry Emery curvature allowing us to prove Harnack and Buser inequalities.
Cite
@article{arxiv.1906.06222,
title = {Large scale Ricci curvature on graphs},
author = {Mark Kempton and Gabor Lippner and Florentin Munch},
journal= {arXiv preprint arXiv:1906.06222},
year = {2019}
}