Eigenvalue estimates on a connected finite graph

Wang, Lin; Zhou, Yu Jie

doi:10.1090/proc/13890

Eigenvalue estimates on a connected finite graph
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by Lin Feng Wang and Yu Jie Zhou PDF

Proc. Amer. Math. Soc. 146 (2018), 4855-4866 Request permission

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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