Sharp modulus of continuity for parabolic equations on manifolds and lower bounds for the first eigenvalue

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Abstract

We derive sharp estimates on the modulus of continuity for solutions of the heat equation on a compact Riemannian manifold with a Ricci curvature bound, in terms of initial oscillation and elapsed time. As an application, we give an easy proof of the optimal lower bound on the first eigenvalue of the Laplacian on such a manifold as a function of diameter.
Original languageEnglish
Pages (from-to)1013 - 1024
Number of pages12
JournalAnalysis & PDE
Volume6
Issue number5
DOIs
Publication statusPublished - 2013
Externally publishedYes

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