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arXiv · 1208.3507

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

Aaron Naber·Daniele Valtorta
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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 $Δ_p$ 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.

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Aaron Naber, Daniele Valtorta. 2014-01-07. Sharp estimates on the first eigenvalue of the p-Laplacian with negative Ricci lower bound. https://doi.org/10.1007/s00209-014-1282-x

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