Sharp estimate on the first eigenvalue of the p-Laplacian

The aim of this paper is to prove the sharp estimate on the first nontrivial eigenvalue of the p-Laplacian on a compact Riemannian manifold with nonnegative Ricci curvature and to characterize the equality case. The estimate applies to manifolds with empty or convex boundary, and in this latter case we also assume Neumann boundary conditions for the p-Laplacian. The main tool used for the proof is a gradient comparison based on a generalized p-Bochner formula.