Complete Pseudohermitian Manifolds with Positive Spectrum

Shu Cheng Chang; Jui Tang Chen; Ting Jung Kuo

doi:10.1007/s12220-013-9414-9

Complete Pseudohermitian Manifolds with Positive Spectrum

Shu Cheng Chang, Jui Tang Chen^*, Ting Jung Kuo

^*Corresponding author for this work

Department of Mathematics

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

Abstract

In this paper, we study complete noncompact pseudohermitian manifolds with positive spectrum of the sub-Laplacian. We prove splitting-type theorems for a class of complete noncompact pseudohermitian manifolds with vanishing torsion whose spectrum of the sub-Laplacian has an optimal positive lower bound. These can be viewed as the CR analogue of theorems of Li–Wang and the equality case of a theorem of Cheng.

Original language	English
Pages (from-to)	92-107
Number of pages	16
Journal	Journal of Geometric Analysis
Volume	25
Issue number	1
DOIs	https://doi.org/10.1007/s12220-013-9414-9
Publication status	Published - 2013 Jan

Keywords

Nonparabolicity
Parabolicity
Positive spectrum
Pseudoharmonic function
Sub-Laplacian
Webster metric

ASJC Scopus subject areas

Geometry and Topology

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10.1007/s12220-013-9414-9

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abstract = "In this paper, we study complete noncompact pseudohermitian manifolds with positive spectrum of the sub-Laplacian. We prove splitting-type theorems for a class of complete noncompact pseudohermitian manifolds with vanishing torsion whose spectrum of the sub-Laplacian has an optimal positive lower bound. These can be viewed as the CR analogue of theorems of Li–Wang and the equality case of a theorem of Cheng.",

keywords = "Nonparabolicity, Parabolicity, Positive spectrum, Pseudoharmonic function, Sub-Laplacian, Webster metric",

author = "Chang, {Shu Cheng} and Chen, {Jui Tang} and Kuo, {Ting Jung}",

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AU - Chen, Jui Tang

AU - Kuo, Ting Jung

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AB - In this paper, we study complete noncompact pseudohermitian manifolds with positive spectrum of the sub-Laplacian. We prove splitting-type theorems for a class of complete noncompact pseudohermitian manifolds with vanishing torsion whose spectrum of the sub-Laplacian has an optimal positive lower bound. These can be viewed as the CR analogue of theorems of Li–Wang and the equality case of a theorem of Cheng.

KW - Nonparabolicity

KW - Parabolicity

KW - Positive spectrum

KW - Pseudoharmonic function

KW - Sub-Laplacian

KW - Webster metric

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Complete Pseudohermitian Manifolds with Positive Spectrum

Abstract

Keywords

ASJC Scopus subject areas

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