Sharp estimates on the first eigenvalue of the p-Laplacian with negative Ricci lower bound

Abstract

We complete the picture of sharp eigenvalue estimates for the p-Laplacian on a compact manifold by providing sharp estimates on the first nonzero eigenvalue of the nonlinear operator ${\Delta }_p$ when the Ricci curvature is bounded from below by a negative constant. We assume that the boundary of the manifold is convex, and put Neumann boundary conditions on it. The proof is based on a refined gradient comparison technique and a careful analysis of the underlying model spaces.

Sign mistake fixed in the proof of the gradient comparison theorem (theorem 5.1 pag 10), and some minor improvements around

References in corpus (1)

• Sharp estimate on the first eigenvalue of the p-Laplacian on compact manifold with nonnegative Ricci curvature

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