Li-Yau gradient estimate and entropy formulae for the CR heat equation in a closed pseudohermitian 3-manifold
Resource
Journal of Differential Geometry, 89(2), 185-216
Journal
Journal of Differential Geometry
Pages
185-216
Date Issued
2011
Date
2011
Author(s)
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.
Type
journal article
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