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

Daniele Valtorta
Springer Verlag, 2014
Article

Résumé

We complete the picture of sharp eigenvalue estimates for the -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.

Official source

https://infoscience.epfl.ch/record/201157?ln=fr

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