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

Shu Cheng Chang; Ting Jung Kuo; Chien Lin; Jingzhi Tie

doi:10.1007/s12220-018-0056-9

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

Shu Cheng Chang, Ting Jung Kuo, Chien Lin, Jingzhi Tie^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

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). 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.

Original language	English
Pages (from-to)	1676-1705
Number of pages	30
Journal	Journal of Geometric Analysis
Volume	29
Issue number	2
DOIs	https://doi.org/10.1007/s12220-018-0056-9
Publication status	Published - 2019 Apr 15

Keywords

CR Bochner formula
Liouville-type theorem
Pseudohermitian Ricci
Pseudohermitian torsion
Ricatti inequality
Sasakain manifold
Sub-Laplacian comparison theorem
Subgradient estimate

ASJC Scopus subject areas

Geometry and Topology

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10.1007/s12220-018-0056-9

Cite this

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title = "CR Sub-Laplacian Comparison and Liouville-Type Theorem in a Complete Noncompact Sasakian Manifold",

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). 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{\textquoteright}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.",

keywords = "CR Bochner formula, Liouville-type theorem, Pseudohermitian Ricci, Pseudohermitian torsion, Ricatti inequality, Sasakain manifold, Sub-Laplacian comparison theorem, Subgradient estimate",

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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

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

Abstract

Keywords

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