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Curvature aspects of graphs


Authors: F. Bauer, F. Chung, Y. Lin and Y. Liu
Journal: Proc. Amer. Math. Soc. 145 (2017), 2033-2042
MSC (2010): Primary 31C20, 31C05
DOI: https://doi.org/10.1090/proc/13145
Published electronically: January 11, 2017
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Abstract: We prove the Lichnerowicz type lower bound estimates for finite connected graphs with positive Ricci curvature lower bound.


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F. Bauer
Affiliation: Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103 Leipzig, Germany

F. Chung
Affiliation: Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093

Y. Lin
Affiliation: Department of Mathematics, Renmin University of China, Beijing 100872, People’s Republic of China

Y. Liu
Affiliation: Institute of Computational Mathematics and Scientific/Engineering Computing. Chinese Academy of Sciences, Beijing 100190, People’s Republic of China

DOI: https://doi.org/10.1090/proc/13145
Keywords: Ricci curvature on graphs, eigenvalue estimate
Received by editor(s): November 18, 2014
Received by editor(s) in revised form: February 5, 2016
Published electronically: January 11, 2017
Additional Notes: The third author was the corresponding author and was supported by the National Natural Science Foundation of China (Grant No. $11271011$), the Fundamental Research Funds for the Central Universities, and the Research Funds of Renmin University of China ($11$XNI$004$)
Communicated by: Lei Ni
Article copyright: © Copyright 2017 American Mathematical Society