Ricci curvature and eigenvalue estimate on locally finite graphs
- Autores: Yong Lin, Shing-Tung Yau
- Localización: Mathematical research letters, ISSN 1073-2780, Vol. 17, Nº 2-3, 2010, págs. 343-356
- Idioma: inglés
- DOI: 10.4310/mrl.2010.v17.n2.a13
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Resumen
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: $$\lambda\ge {1\over d D(\exp( d D+1)-1)},$$ where $d$ is the weighted degree of $G$, and $D$ is the diameter of $G$.
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