Lower bounds for the first eigenvalue of the [formula omitted]-Laplacian on compact manifolds with positive Ricci curvature

Abstract

We give some lower bounds for the first eigenvalue of the p -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.