TY - JOUR
T1 - CR Sub-Laplacian Comparison and Liouville-Type Theorem in a Complete Noncompact Sasakian Manifold
AU - Chang, Shu Cheng
AU - Kuo, Ting Jung
AU - Lin, Chien
AU - Tie, Jingzhi
N1 - Funding Information:
The authors warmly thank the referee for his/her useful remarks and questions that have greatly helped to improve the paper. S.-C. Chang would like to express his gratitude to S.-T. Yau for the inspiration, C.-S. Lin for constant encouragement and supports, and J.-P. Wang for his inspiration on sub-Laplacian comparison geometry. Part of the project was done during J. Tie’s visits to Taida Institute for Mathematical Sciences (TIMS) and he would like to thank TIMS for support.
Funding Information:
Shu-Cheng Chang, Ting-Jung Kuo, and Chien Lin—research supported in part by the MOST of Taiwan.
Publisher Copyright:
© 2018, Mathematica Josephina, Inc.
PY - 2019/4/15
Y1 - 2019/4/15
N2 - In this paper, we first obtain the sub-Laplacian comparison theorem in a complete noncompact pseudohermitian manifold of vanishing torsion (i.e., Sasakian manifold). Second, we derive the subgradient estimate for positive pseudoharmonic functions in a complete noncompact pseudohermitian manifold which satisfies the CR sub-Laplacian comparison property. It functions as the CR analog of Yau’s gradient estimate. As a consequence, we have the natural CR analog of Liouville-type theorems in a complete noncompact Sasakian manifold of nonnegative pseudohermitian Ricci curvature tensors.
AB - In this paper, we first obtain the sub-Laplacian comparison theorem in a complete noncompact pseudohermitian manifold of vanishing torsion (i.e., Sasakian manifold). Second, we derive the subgradient estimate for positive pseudoharmonic functions in a complete noncompact pseudohermitian manifold which satisfies the CR sub-Laplacian comparison property. It functions as the CR analog of Yau’s gradient estimate. As a consequence, we have the natural CR analog of Liouville-type theorems in a complete noncompact Sasakian manifold of nonnegative pseudohermitian Ricci curvature tensors.
KW - CR Bochner formula
KW - Liouville-type theorem
KW - Pseudohermitian Ricci
KW - Pseudohermitian torsion
KW - Ricatti inequality
KW - Sasakain manifold
KW - Sub-Laplacian comparison theorem
KW - Subgradient estimate
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U2 - 10.1007/s12220-018-0056-9
DO - 10.1007/s12220-018-0056-9
M3 - Article
AN - SCOPUS:85049071132
SN - 1050-6926
VL - 29
SP - 1676
EP - 1705
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
IS - 2
ER -