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Matrix Li–Yau–Hamilton inequality for the CR heat equation in pseudohermitian (2n+1) -manifolds

Shu-Cheng Chang National Taiwan University Yen-Wen Fan National Taiwan University Jingzhi Tie University of Georgia Chin-Tung Wu National Pingtung University of Education

Differential Geometry mathscidoc:1701.10020

Distinguished Paper Award in 2017

Mathematische Annalen, 360, (1), 266-306, 2014.10
In this paper, we first derive the CR analogue of matrix Li–Yau–Hamilton inequality for the positive solution to the CR heat equation in a closed pseudohermitian (2n + 1)-manifold with nonnegative bisectional curvature and bitorsional tensor. We then obtain the CR Li–Yau gradient estimate in the Heisenberg group. We apply this CR gradient estimate and extend the CR matrix Li–Yau–Hamilton inequality to the case of the Heisenberg group. As a consequence, we derive the Hessian comparison property for the Heisenberg group.
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@inproceedings{shu-cheng2014matrix,
  title={Matrix Li–Yau–Hamilton inequality for the CR heat equation in pseudohermitian (2n+1) -manifolds},
  author={Shu-Cheng Chang, Yen-Wen Fan, Jingzhi Tie, and Chin-Tung Wu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170116232731793477113},
  booktitle={Mathematische Annalen},
  volume={360},
  number={1},
  pages={266-306},
  year={2014},
}
Shu-Cheng Chang, Yen-Wen Fan, Jingzhi Tie, and Chin-Tung Wu. Matrix Li–Yau–Hamilton inequality for the CR heat equation in pseudohermitian (2n+1) -manifolds. 2014. Vol. 360. In Mathematische Annalen. pp.266-306. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170116232731793477113.
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