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Proceedings of the American Mathematical Society

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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: Based on gradient estimates of the eigenfunction, we prove lower bound estimates for the first nonzero eigenvalue of the $ \mu $-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