English

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