Liouville property and non-negative Ollivier curvature on graphs

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.

Added examples, fixed typos

References in corpus (6)

• Eigenvalue ratios of nonnegatively curved graphs
• The Graph Curvature Calculator and the curvatures of cubic graphs
• Equivalent Properties of CD Inequality on Graph
• Gradient estimates, Bakry-Emery Ricci curvature and ellipticity for unbounded graph Laplacians
• Liouville theorem for bounded harmonic functions on manifolds and graphs satisfying non-negative curvature dimension condition
• Buser's inequality on infinite graphs

Cited by in corpus (2)

• Every Salami has two ends
• Graphs with nonnegative Ricci curvature and maximum degree at most 3