CR Sub-Laplacian Comparison and Liouville-type Theorem in a Complete Noncompact Sasakian Manifold

2015/06/10 by Shu-Cheng Chang, Chang, Shu-Cheng, Ting-Jung Kuo +5
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #math.AP #math.DG #math.GT

paper · pdf · doi:10.48550/arxiv.1506.03270

arxiv created 2018/01/31 · arxiv updated 2018/02/01

Abstract

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 analog of Yau's 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.

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