### 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 |
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Pages (from-to) | 185-216 |

Number of pages | 32 |

Journal | Journal of Differential Geometry |

Volume | 89 |

Issue number | 2 |

Publication status | Published - 2011 Dec |

Externally published | Yes |

### ASJC Scopus subject areas

- Analysis
- Algebra and Number Theory
- Geometry and Topology

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## Cite this

Chang, S. C., Kuo, T. J., & Lai, S. H. (2011). Li-yau gradient estimate and entropy formulae for the cr heat equation in a closed pseudohermitian 3-manifold.

*Journal of Differential Geometry*,*89*(2), 185-216.