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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title = "Complete Pseudohermitian Manifolds with Positive Spectrum",

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\}",

note = "Publisher Copyright: {\textcopyright} 2013, Mathematica Josephina, Inc.",

year = "2013",

month = jan,

doi = "10.1007/s12220-013-9414-9",

language = "English",

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AU - Chang, Shu Cheng

AU - Chen, Jui Tang

AU - Kuo, Ting Jung

PY - 2013/1

Y1 - 2013/1

N2 - 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.

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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UR - https://www.scopus.com/pages/publications/84876181139#tab=citedBy

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DO - 10.1007/s12220-013-9414-9

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EP - 107

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 1

ER -

Complete Pseudohermitian Manifolds with Positive Spectrum

Abstract

Keywords

ASJC Scopus subject areas

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