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Cr sub-laplacian comparison and liouville-type theorem in a complete noncompact sasakian manifold

Shu-Cheng Chang National Taiwan University Ting-Jung Kuo National Taiwan Normal University Chien Lin National Tsinghua University Jingzhi Tie University of Georgia

Differential Geometry mathscidoc:1801.10001

In this paper, we first obtain the sub-Laplacian comparison theorem in a complete noncompact pseudohermitian manifold of vanishing torsion (i.e. Sasakian manifold). Secondly, we derive the sub-gradient estimate for positive pseudoharmonic functions in a complete noncompact pseudohermitian manifold which satisfies the CR sub-Laplacian comparison property. It is served as the CR analogue of Yauís gradient estimate. As a consequence, we have the natural CR analogue of Liouville-type theorems in a complete noncompact Sasakian manifold of nonnegative pseudohermitian Ricci curvature tensors.
CR Bochner formula, Subgradient estimate, Sub-Laplacian comparison theorem, Liouvile-type theorem, Pseudohermtian Ricci, Pseudohermitian torsion, Ricatti inequality, Sasakain manifold.
[ Download ] [ 2018-01-28 15:08:15 uploaded by scchang ] [ 743 downloads ] [ 0 comments ] 
@inproceedings{shu-chengcr,
  title={CR SUB-LAPLACIAN COMPARISON AND LIOUVILLE-TYPE THEOREM IN A COMPLETE NONCOMPACT SASAKIAN MANIFOLD},
  author={Shu-Cheng Chang, Ting-Jung Kuo, Chien Lin, and Jingzhi Tie},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180128150815982698911},
}
Shu-Cheng Chang, Ting-Jung Kuo, Chien Lin, and Jingzhi Tie. CR SUB-LAPLACIAN COMPARISON AND LIOUVILLE-TYPE THEOREM IN A COMPLETE NONCOMPACT SASAKIAN MANIFOLD. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180128150815982698911.
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