Sharp modulus of continuity for parabolic equations on manifolds and lower bounds for the first eigenvalue
Analysis of PDEs
2016-01-20 v1 Differential Geometry
Spectral Theory
Abstract
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.
Keywords
Cite
@article{arxiv.1204.5079,
title = {Sharp modulus of continuity for parabolic equations on manifolds and lower bounds for the first eigenvalue},
author = {Ben Andrews and Julie Clutterbuck},
journal= {arXiv preprint arXiv:1204.5079},
year = {2016}
}