Sharp estimates on the first eigenvalue of the p-Laplacian with negative Ricci lower bound
Differential Geometry
2014-02-04 v4 Analysis of PDEs
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 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.
Keywords
Cite
@article{arxiv.1208.3507,
title = {Sharp estimates on the first eigenvalue of the p-Laplacian with negative Ricci lower bound},
author = {Aaron Naber and Daniele Valtorta},
journal= {arXiv preprint arXiv:1208.3507},
year = {2014}
}
Comments
Sign mistake fixed in the proof of the gradient comparison theorem (theorem 5.1 pag 10), and some minor improvements around