Liouville property and non-negative Ollivier curvature on graphs

2019/03/26 by Jürgen Jost, Jost, Jürgen, Florentin Münch +3 · 2 citations
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1903.10796

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.

Citations

• Ricci curvature of Markov chains on metric spaces

Cited by

• Bounded-degree graphs of non-negative Ollivier-Ricci curvature have subexponential growth and diffusive random walk
• Graphs with nonnegative Ricci curvature and maximum degree at most 3

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