Sharp estimate on the first eigenvalue of the p-Laplacian on compact manifold with nonnegative Ricci curvature
Differential Geometry
2014-01-08 v8 Classical Analysis and ODEs
Abstract
We prove the sharp estimate on the first nonzero eigenvalue of the p-laplacian on a compact Riemannian manifold with nonnegative Ricci curvature and possibly with convex boundary (in this case we assume Neumann b.c. on the p-laplacian). The proof is based on a gradient comparison theorem. We will also charachterize the equality case in the estimate.
Keywords
Cite
@article{arxiv.1102.0539,
title = {Sharp estimate on the first eigenvalue of the p-Laplacian on compact manifold with nonnegative Ricci curvature},
author = {Daniele Valtorta},
journal= {arXiv preprint arXiv:1102.0539},
year = {2014}
}
Comments
Added Remark 4.5 to address a regularity issue when 1<p<2