Buser's inequality on infinite graphs

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:475

Article

Liu, Shuang^1,2 

[1] Tsinghua Univ, Yau Math Sci Ctr, Beijing, Peoples R China

[2] Renmin Univ China, Sch Math, Beijing, Peoples R China

关键词: Buser's inequality;    Infinite graph;    Curvature-dimension inequality;    Cheeger constants;   

DOI  :  10.1016/j.jmaa.2019.03.023

来源: Elsevier

【 摘 要 】

In this paper, we establish Buser type inequalities, i.e., upper bounds for eigenvalues in terms of Cheeger constants. We prove the Buser's inequality for an infinite but locally finite connected graph with Ricci curvature lower bounds. Furthermore, we derive that the graph with positive curvature is finite, especially for unbounded Laplacians. By proving Poincare inequality, we obtain a lower bound for Cheeger constant in terms of positive curvature. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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