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

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Abstract

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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Acknowledgments

The third named author would like to express his thanks to Taida Institute for Mathematical Sciences (TIMS), National Taiwan University. Part of the project was done during his visit to TIMS.

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Authors and Affiliations

  1. Department of Mathematics, Taida Institute for Mathematical Sciences (TIMS), National Taiwan University, Taipei,  10617, Taiwan

    Shu-Cheng Chang & Yen-Wen Fan

  2. Department of Mathematics, University of Georgia, Athens, GA,  30602-7403, USA

    Jingzhi Tie

  3. Department of Applied Mathematics, National Pingtung University of Education, Pingtung,  90003, Taiwan

    Chin-Tung Wu

Authors
  1. Shu-Cheng Chang
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  2. Yen-Wen Fan
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  3. Jingzhi Tie
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  4. Chin-Tung Wu
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Correspondence to Shu-Cheng Chang.

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Research supported in part by NSC of Taiwan.

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Chang, SC., Fan, YW., Tie, J. et al. Matrix Li–Yau–Hamilton inequality for the CR heat equation in pseudohermitian \((2n+1)\)-manifolds. Math. Ann. 360, 267–306 (2014). https://doi.org/10.1007/s00208-014-1036-4

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  • DOI: https://doi.org/10.1007/s00208-014-1036-4

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