### 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 |

### Fingerprint

### ASJC Scopus subject areas

- Analysis
- Algebra and Number Theory
- Geometry and Topology

### Cite this

*Journal of Differential Geometry*,

*89*(2), 185-216.

**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.

Research output: Contribution to journal › Article

*Journal of Differential Geometry*, vol. 89, no. 2, pp. 185-216.

}

TY - JOUR

T1 - Li-yau gradient estimate and entropy formulae for the cr heat equation in a closed pseudohermitian 3-manifold

AU - Chang, Shu Cheng

AU - Kuo, Ting Jung

AU - Lai, Sin Hua

PY - 2011/12

Y1 - 2011/12

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=84862968723&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84862968723&partnerID=8YFLogxK

M3 - Article

VL - 89

SP - 185

EP - 216

JO - Journal of Differential Geometry

JF - Journal of Differential Geometry

SN - 0022-040X

IS - 2

ER -