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

^*此作品的通讯作者

科研成果: 期刊稿件 › 文章 › 同行评审

17 引用（Scopus）

摘要

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.

源语言	英语
文章编号	106822
期刊	Advances in Mathematics
卷	357
DOI	https://doi.org/10.1016/j.aim.2019.106822
出版状态	已出版 - 1 12月 2019
已对外发布	是

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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, 文章 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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year = "2019",

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doi = "10.1016/j.aim.2019.106822",

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AU - Gong, Chao

AU - Lin, Yong

AU - Liu, Shuang

AU - Yau, Shing Tung

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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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VL - 357

JO - Advances in Mathematics

JF - Advances in Mathematics

M1 - 106822

ER -

Li-Yau inequality for unbounded Laplacian on graphs

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