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arXiv · 1801.06021

Li-Yau inequality for unbounded Laplacian on graphs

Chao Gong·Yong Lin·Shuang Liu·Shing-Tung Yau
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Abstract

In this paper, we derive Li-Yau inequality for unbounded Laplacian on complete weighted graphs with the assumption of the curvature-dimension inequality $CDE'(n,K)$, 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 first kind of results on this direction for unbounded Laplacian on graphs.

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Chao Gong, Yong Lin, Shuang Liu, Shing-Tung Yau. 2018-01-24. Li-Yau inequality for unbounded Laplacian on graphs. https://arxiv.org/abs/1801.06021

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