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Li-Yau inequality for unbounded Laplacian on graphs

Chao Gong Yong Lin Shuang Liu Shing-Tung Yau

Differential Geometry mathscidoc:1912.43669

Advances in Mathematics, 357, 106822, 2019.12
In this paper, we derive Li-Yau inequality for unbounded Laplacian on complete weighted graphs with the assumption of the curvature dimension inequality C D E(n, K), which can be regarded as a notion of curvature on graphs. Furthermore, we obtain some applications of Li-Yau inequality, including Harnack inequality, heat kernel bounds and Cheng's eigenvalue estimate. These are the first kind of results in this direction for unbounded Laplacian on graphs.
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@inproceedings{chao2019li-yau,
  title={Li-Yau inequality for unbounded Laplacian on graphs},
  author={Chao Gong, Yong Lin, Shuang Liu, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204845014829233},
  booktitle={Advances in Mathematics},
  volume={357},
  pages={106822},
  year={2019},
}
Chao Gong, Yong Lin, Shuang Liu, and Shing-Tung Yau. Li-Yau inequality for unbounded Laplacian on graphs. 2019. Vol. 357. In Advances in Mathematics. pp.106822. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204845014829233.
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