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

Aaron Naber, Daniele Valtorta*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

28 Scopus citations

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 Δp 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.

Original languageEnglish (US)
Pages (from-to)867-891
Number of pages25
JournalMathematische Zeitschrift
Volume277
Issue number3-4
DOIs
StatePublished - Aug 2014

ASJC Scopus subject areas

  • Mathematics(all)

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