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

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13 Citations (Scopus)


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
Issue number2
Publication statusPublished - 2011 Dec
Externally publishedYes


ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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