Eigenvalue estimates on a connected finite graph
Authors:
Lin Feng Wang and Yu Jie Zhou
Journal:
Proc. Amer. Math. Soc. 146 (2018), 4855-4866
MSC (2010):
Primary 53C21, 05C99
DOI:
https://doi.org/10.1090/proc/13890
Published electronically:
August 10, 2018
MathSciNet review:
3856152
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Abstract | References | Similar Articles | Additional Information
Abstract: Based on gradient estimates of the eigenfunction, we prove lower bound estimates for the first nonzero eigenvalue of the -Laplacian on a connected finite graph through the curvature-dimension conditions. These estimates are parallel to the results on compact Riemannian manifolds with the Ricci curvature bounded from below.
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Additional Information
Lin Feng Wang
Affiliation:
School of Science, Nantong University, Nantong 226007, Jiangsu, People’s Republic of China
Email:
wlf711178@126.com
Yu Jie Zhou
Affiliation:
School of Science, Nantong University, Nantong 226007, Jiangsu, People’s Republic of China
Email:
1109920674@qq.com
DOI:
https://doi.org/10.1090/proc/13890
Keywords:
Connected finite graph,
$CDE(m,K)$ condition,
$CD(m,K)$ condition,
gradient estimate,
eigenvalue
Received by editor(s):
February 27, 2017
Received by editor(s) in revised form:
July 6, 2017
Published electronically:
August 10, 2018
Additional Notes:
The authors were supported by the NSF of Jiangsu Province (BK20141235)
Communicated by:
Guofang Wei
Article copyright:
© Copyright 2018
American Mathematical Society