Lower bounds for the first eigenvalue of the pp-Laplacian on compact manifolds with positive Ricci curvature

We give some lower bounds for the first eigenvalue of the pp-Laplace operator on compact Riemannian manifolds with positive (or non-negative) Ricci curvature in terms of diameter of the manifolds. For compact manifolds with boundary, we consider the Dirichlet eigenvalue with some proper geometric hypothesis.