Gradient estimates, Bakry-Emery Ricci curvature and ellipticity for unbounded graph Laplacians

2018/07/26 by Matthias Keller, Keller, Matthias, Florentin Münch +1 · 2 citations
Mathematics · #05C81 #35K05 #53C21 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1807.10181

openalex publication_date 2018/07/26 · openalex created_date 2018/08/03 · openalex updated_date 2026/07/28

Abstract

In this article, we prove gradient estimates under Bakry-Emery curvature bounds for unbounded graph Laplacians which satisfy an ellipticity assumption. As applications, we study completeness and finiteness of stochastically complete graphs under Bakry-Emery curvature bounds.

Citations

• Gradient flows of the entropy for finite Markov chains
• Coarse Ricci curvature for continuous-time Markov processes
• One example about the relationship between the CD inequality and CDE' inequality
• Li-Yau inequality for unbounded Laplacian on graphs

Cited by

• Bounded-degree graphs of non-negative Ollivier-Ricci curvature have subexponential growth and diffusive random walk
• Bakry-Émery curvature on graphs as an eigenvalue problem

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