The first eigenfunctions and eigenvalue of the p-Laplacian on Finsler manifolds

This paper proves that the first eigenfunctions of the Finsler p-Lapalcian are C^1,α. Using a gradient comparison theorem and one-dimensional model, we obtain the sharp lower bound of the first Neumann and closed eigenvalue of the p-Laplacian on a compact Finsler manifold with nonnegative weighted Ricci curvature, on which a lower bound of the first Dirichlet eigenvalue of the p-Laplacian is also obtained.