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2013 Sharp modulus of continuity for parabolic equations on manifolds and lower bounds for the first eigenvalue
Ben Andrews, Julie Clutterbuck
Anal. PDE 6(5): 1013-1024 (2013). DOI: 10.2140/apde.2013.6.1013

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.

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Ben Andrews. Julie Clutterbuck. "Sharp modulus of continuity for parabolic equations on manifolds and lower bounds for the first eigenvalue." Anal. PDE 6 (5) 1013 - 1024, 2013. https://doi.org/10.2140/apde.2013.6.1013

Information

Received: 1 April 2012; Accepted: 21 May 2013; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1282.35099
MathSciNet: MR3125548
Digital Object Identifier: 10.2140/apde.2013.6.1013

Subjects:
Primary: 35K05, 35K55, 35P15

Rights: Copyright © 2013 Mathematical Sciences Publishers

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