A sharp lower bound for the first eigenvalue on Finsler manifolds with nonnegative weighted Ricci curvature

Let (M, F) be an n-dimensional compact Finsler manifold without boundary or with a convex boundary and lambda(1) be the first (nonzero) closed or Neumann eigenvalue of the Finsler Laplacian on M with nonnegative weighted Ricci curvature. In this paper, we prove that lambda(1) >= pi(2)/d(2), where d is the diameter of M, and that the equality holds if and only if M is a 1-dimensional circle or a 1-dimensional segment, which generalize the well-known Zhong-Yang's sharp estimate in Riemannian geometry (Zhong and Yang, 1984). (C) 2015 Elsevier Ltd. All rights reserved.