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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

21 Citations (Scopus)

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.

Original language	English
Pages (from-to)	185-216
Number of pages	32
Journal	Journal of Differential Geometry
Volume	89
Issue number	2
DOIs	https://doi.org/10.4310/jdg/1324477409
Publication status	Published - 2011
Externally published	Yes

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Geometry and Topology

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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.",

author = "Chang, {Shu Cheng} and Kuo, {Ting Jung} and Lai, {Sin Hua}",

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AU - Chang, Shu Cheng

AU - Kuo, Ting Jung

AU - Lai, Sin Hua

PY - 2011

Y1 - 2011

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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

Abstract

ASJC Scopus subject areas

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