Li-yau gradient estimate and entropy formulae for the cr heat equation in a closed pseudohermitian 3-manifold

Shu-Cheng Chang National Taiwan University Ting-Jung Kuo Taida Institute for Mathematical Sciences Sin-Hua Lai National Central University

Differential Geometry mathscidoc:1609.10238

Journal of Differential Geometry, 89, (2), 185-216, 2011
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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@inproceedings{shu-cheng2011li-yau,
  title={LI-YAU GRADIENT ESTIMATE AND ENTROPY FORMULAE FOR THE CR HEAT EQUATION IN A CLOSED PSEUDOHERMITIAN 3-MANIFOLD},
  author={Shu-Cheng Chang, Ting-Jung Kuo, and Sin-Hua Lai},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913210333812603899},
  booktitle={Journal of Differential Geometry},
  volume={89},
  number={2},
  pages={185-216},
  year={2011},
}
Shu-Cheng Chang, Ting-Jung Kuo, and Sin-Hua Lai. LI-YAU GRADIENT ESTIMATE AND ENTROPY FORMULAE FOR THE CR HEAT EQUATION IN A CLOSED PSEUDOHERMITIAN 3-MANIFOLD. 2011. Vol. 89. In Journal of Differential Geometry. pp.185-216. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913210333812603899.
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