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

Research output: Contribution to journalArticle

12 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 languageEnglish
Pages (from-to)185-216
Number of pages32
JournalJournal of Differential Geometry
Volume89
Issue number2
Publication statusPublished - 2011 Dec
Externally publishedYes

Fingerprint

Gradient Estimate
Heat Equation
Subgradient
Entropy
Closed
Estimate
Harnack Inequality
Heat Kernel
Logarithm
Positive Solution
Upper bound

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

Cite this

Li-yau gradient estimate and entropy formulae for the cr heat equation in a closed pseudohermitian 3-manifold. / Chang, Shu Cheng; Kuo, Ting Jung; Lai, Sin Hua.

In: Journal of Differential Geometry, Vol. 89, No. 2, 12.2011, p. 185-216.

Research output: Contribution to journalArticle

Chang, Shu Cheng ; Kuo, Ting Jung ; Lai, Sin Hua. / Li-yau gradient estimate and entropy formulae for the cr heat equation in a closed pseudohermitian 3-manifold. In: Journal of Differential Geometry. 2011 ; Vol. 89, No. 2. pp. 185-216.
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