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

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

2012-04-23

arxiv.org/abs/1204.5079v1

Mathematics

Analysis of PDEs

Scientific paper

We derive sharp estimates on 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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