Liouville property and non-negative Ollivier curvature on graphs
Differential Geometry
2025-04-04 v2
Abstract
For graphs with non-negative Ollivier curvature, we prove the Liouville property, i.e., every bounded harmonic function is constant. Moreover, we improve Ollivier's results on concentration of the measure under positive Ollivier curvature.
Cite
@article{arxiv.1903.10796,
title = {Liouville property and non-negative Ollivier curvature on graphs},
author = {Jürgen Jost and Florentin Münch and Christian Rose},
journal= {arXiv preprint arXiv:1903.10796},
year = {2025}
}
Comments
Added examples, fixed typos