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October 2011 Li-Yau gradient estimate and entropy formulae for the CR heat equation in a closed pseudohermitian 3-manifold
Shu-Cheng Chang, Ting-Jung Kuo, Sin-Hua Lai
J. Differential Geom. 89(2): 185-216 (October 2011). DOI: 10.4310/jdg/1324477409

Abstract

In this paper, we derive two subgradient estimates of the CR heat equation in a closed pseudohermitian 3-manifold which are served as the CR version of the Li-Yau gradient estimate. With its applications, we first get a subgradient estimate of the logarithm of the positive solution of the CR heat equation. Secondly, we have the Harnack inequality and upper bound estimate for the heat kernel. Finally, we obtain Perelman-type entropy formulae for the CR heat equation.

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Shu-Cheng Chang. Ting-Jung Kuo. Sin-Hua Lai. "Li-Yau gradient estimate and entropy formulae for the CR heat equation in a closed pseudohermitian 3-manifold." J. Differential Geom. 89 (2) 185 - 216, October 2011. https://doi.org/10.4310/jdg/1324477409

Information

Published: October 2011
First available in Project Euclid: 21 December 2011

zbMATH: 1264.32030
MathSciNet: MR2863916
Digital Object Identifier: 10.4310/jdg/1324477409

Rights: Copyright © 2011 Lehigh University

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Vol.89 • No. 2 • October 2011
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