Some new lower bounds of the first eigenvalue on Finsler manifolds

Abstract

We establish some unified lower bounds for the first Neumann and closed eigenvalues of the Finsler-Laplacian on compact Finsler manifolds under the weighted Ricci curvature conditions, which extend some recent theorems on the first eigenvalue of the Riemannian-Laplacian. Moreover, the Lichnerowicz type lower bound for the first Dirichlet eigenvalue of the Finsler-Laplacian is also obtained.