Cr Li-Yau gradient estimate for witten Laplacian via Bakry-Emery Pseudohermitian Ricci Curvature

Der Chen Chang, Shu Cheng Chang, Ting Jung Kuo, Sin Hua Lai

Research output: Contribution to journalArticle


In this paper, we derive the sub-gradient estimate of the CR heat equation associated with the Witten sub-Laplacian via the Bakry-Emery Pseudohermitian Ricci Curvature. With its applications, we first get a Harnack inequality for the positive solution of this CR heat equation in a closed pseudohermitian (2n + 1)-manifold. Secondly, we obtain Perelman-type linear entropy formulae for this CR heat equation.

Original languageEnglish
Pages (from-to)223-256
Number of pages34
JournalAsian Journal of Mathematics
Issue number2
Publication statusPublished - 2018 Jan 1
Externally publishedYes



  • Bakry-Emery Pseudohermitian Ricci Curvature
  • CR heat equation
  • Harnack inequality
  • Li-Yau gradient estimate
  • Perelman Entropy formulae
  • Pseudohermitian manifold
  • Witten Laplacian

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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