Lower bound of coarse Ricci curvature on metric measure spaces and eigenvalues of Laplacian

Abstract

We prove that a Bishop-Gromov inequality gives a lower bound of coarse Ricci curvature. We also have an estimate of the eigenvalues of the Laplacian by a lower bound of coarse Ricci curvature.

8 pages, with 2 figures

References in corpus (2)

• Metric measure spaces with Riemannian Ricci curvature bounded from below
• Ollivier's Ricci curvature, local clustering and curvature dimension inequalities on graphs