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

doi:10.4310/jdg/1324477409

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

^*此作品的通信作者

研究成果: 雜誌貢獻 › 期刊論文 › 同行評審

22 引文斯高帕斯（Scopus）

摘要

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.

原文	英語
頁（從 - 到）	185-216
頁數	32
期刊	Journal of Differential Geometry
卷	89
發行號	2
DOIs	https://doi.org/10.4310/jdg/1324477409
出版狀態	已發佈 - 2011
對外發佈	是

ASJC Scopus subject areas

分析
代數與數理論
幾何和拓撲

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

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