Li-Yau inequality for unbounded Laplacian on graphs

Chao Gong; Yong Lin; Shuang Liu; Shing Tung Yau

doi:10.1016/j.aim.2019.106822

Li-Yau inequality for unbounded Laplacian on graphs

Chao Gong, Yong Lin, Shuang Liu^*, Shing Tung Yau

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

17 Citations (Scopus)

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 the first kind of results in this direction for unbounded Laplacian on graphs.

Original language	English
Article number	106822
Journal	Advances in Mathematics
Volume	357
DOIs	https://doi.org/10.1016/j.aim.2019.106822
Publication status	Published - 1 Dec 2019
Externally published	Yes

Keywords

Cheng's eigenvalue estimate
Heat kernel
Li-Yau inequality on graphs
Unbounded Laplacians

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10.1016/j.aim.2019.106822

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Gong, C., Lin, Y., Liu, S., & Yau, S. T. (2019). Li-Yau inequality for unbounded Laplacian on graphs. Advances in Mathematics, 357, Article 106822. https://doi.org/10.1016/j.aim.2019.106822

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title = "Li-Yau inequality for unbounded Laplacian on graphs",

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 the first kind of results in this direction for unbounded Laplacian on graphs.",

keywords = "Cheng's eigenvalue estimate, Heat kernel, Li-Yau inequality on graphs, Unbounded Laplacians",

author = "Chao Gong and Yong Lin and Shuang Liu and Yau, {Shing Tung}",

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AU - Lin, Yong

AU - Liu, Shuang

AU - Yau, Shing Tung

PY - 2019/12/1

Y1 - 2019/12/1

N2 - 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 the first kind of results in this direction for unbounded Laplacian on graphs.

AB - 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 the first kind of results in this direction for unbounded Laplacian on graphs.

KW - Cheng's eigenvalue estimate

KW - Heat kernel

KW - Li-Yau inequality on graphs

KW - Unbounded Laplacians

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JO - Advances in Mathematics

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ER -

Li-Yau inequality for unbounded Laplacian on graphs

Abstract

Keywords

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