English

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.

Keywords

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