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

Let (M,F)(M,F) be an nn-dimensional compact Finsler manifold without boundary or with a convex boundary and λ1λ1 be the first (nonzero) closed or Neumann eigenvalue of the Finsler Laplacian on MM with nonnegative weighted Ricci curvature. In this paper, we prove that λ1≥π2d2, where dd is the diameter of MM, and that the equality holds if and only if MM is a 11-dimensional circle or a 11-dimensional segment, which generalize the well-known Zhong–Yang’s sharp estimate in Riemannian geometry (Zhong and Yang, 1984).