Ricci curvature and eigenvalue estimate on locally finite graphs

Yong Lin Shing-Tung Yau

Differential Geometry mathscidoc:1912.43493

Mathematical research letters, 17, (2), 343-356, 2010.3
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: 1 dD (exp (dD+ 1) 1)
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  title={Ricci curvature and eigenvalue estimate on locally finite graphs},
  author={Yong Lin, and Shing-Tung Yau},
  booktitle={Mathematical research letters},
Yong Lin, and Shing-Tung Yau. Ricci curvature and eigenvalue estimate on locally finite graphs. 2010. Vol. 17. In Mathematical research letters. pp.343-356. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203604155582057.
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