Lower bounds for the first eigenvalue of the p-Laplace operator on compact manifolds with nonnegative Ricci curvature

We present some lower bound estimates for the first eigenvalue of p-Laplace operators on compact Riemannian manifolds with quasi-positive (or nonnegative) Ricci curvature in terms of diameter of the manifolds. For compact manifolds with boundary, we consider the Dirichlet eigenvalue problem with some proper hypothesis.