Ricci curvature and eigenvalue estimate on locally finite graphs

2010/01/01 by Yong Lin, Shing–Tung Yau · 2 citations
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Advanced Differential Geometry Research #Geometry and complex manifolds #Mathematics #Ricci curvature #Curvature #Eigenvalues and eigenvectors #Ricci flow #Pure mathematics #Mathematical analysis #Geometry

paper · pdf · doi:10.4310/mrl.2010.v17.n2.a13

openalex publication_date 2010/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11

Abstract

We give a generalizations of lower Ricci curvature bound in the framework of graphs. We prove that the Ricci curvature in the sense of Bakry and Emery is bounded below by -1 on locally finite graphs. The Ricci flat graph in the sense of Chung and Yau is proved to be a graph with Ricci curvature bounded below by zero. We also get an estimate for the eigenvalue of Laplace operator on finite graphs:

Citations

• Spectral graph theory [CBMS Conference on Recent Advances in Spectral Graph Theory held at California State University at Fresno, June 6 - 10. 1994]
• Ricci curvature for metric-measure spaces via optimal transport
• On the parabolic kernel of the Schrödinger operator
• Ricci curvature of Markov chains on metric spaces

Cited by

• Ricci curvature of graphs
• Shing-Tung Yau [wikipedia]

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