Buser's inequality on infinite graphs

Shuang Liu

doi:10.1016/j.jmaa.2019.03.023

Buser's inequality on infinite graphs

Shuang Liu

科研成果: 期刊稿件 › 文章 › 同行评审

5 引用（Scopus）

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 Poincaré inequality, we obtain a lower bound for Cheeger constant in terms of positive curvature.

源语言	英语
页（从-至）	1416-1426
页数	11
期刊	Journal of Mathematical Analysis and Applications
卷	475
期	2
DOI	https://doi.org/10.1016/j.jmaa.2019.03.023
出版状态	已出版 - 15 7月 2019
已对外发布	是

访问文件

10.1016/j.jmaa.2019.03.023

其它文件与链接

链接到 Scopus 的出版物

引用此

Liu, S. (2019). Buser's inequality on infinite graphs. Journal of Mathematical Analysis and Applications, 475(2), 1416-1426. https://doi.org/10.1016/j.jmaa.2019.03.023

@article{4403b2c4439842b082343195819be71e,

title = "Buser's inequality on infinite graphs",

abstract = "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 Poincar{\'e} inequality, we obtain a lower bound for Cheeger constant in terms of positive curvature.",

keywords = "Buser's inequality, Cheeger constants, Curvature-dimension inequality, Infinite graph",

author = "Shuang Liu",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

year = "2019",

month = jul,

day = "15",

doi = "10.1016/j.jmaa.2019.03.023",

language = "English",

volume = "475",

pages = "1416--1426",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - Buser's inequality on infinite graphs

AU - Liu, Shuang

PY - 2019/7/15

Y1 - 2019/7/15

N2 - 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 Poincaré inequality, we obtain a lower bound for Cheeger constant in terms of positive curvature.

AB - 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 Poincaré inequality, we obtain a lower bound for Cheeger constant in terms of positive curvature.

KW - Buser's inequality

KW - Cheeger constants

KW - Curvature-dimension inequality

KW - Infinite graph

UR - http://www.scopus.com/inward/record.url?scp=85063261197&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2019.03.023

DO - 10.1016/j.jmaa.2019.03.023

M3 - Article

AN - SCOPUS:85063261197

SN - 0022-247X

VL - 475

SP - 1416

EP - 1426

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Buser's inequality on infinite graphs

摘要

访问文件

其它文件与链接

指纹

引用此