The CR Paneitz operator and the stability of CR pluriharmonic functions

Jeffrey S. Case; Sagun Chanillo; Paul Yang

doi:10.1016/j.aim.2015.10.002

The CR Paneitz operator and the stability of CR pluriharmonic functions

Jeffrey S. Case, Sagun Chanillo, Paul Yang

Mathematics

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

10 Scopus citations

Abstract

We give a condition which ensures that the Paneitz operator of an embedded three-dimensional CR manifold is nonnegative and has kernel consisting only of the CR pluriharmonic functions. Our condition requires uniform positivity of the Webster scalar curvature and the stability of the CR pluriharmonic functions for a real analytic deformation. As an application, we show that the real ellipsoids in C2 are such that the CR Paneitz operator is nonnegative with kernel consisting only of the CR pluriharmonic functions.

Original language	English (US)
Pages (from-to)	109-122
Number of pages	14
Journal	Advances in Mathematics
Volume	287
DOIs	https://doi.org/10.1016/j.aim.2015.10.002
State	Published - Jan 10 2016

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

CR Paneitz operator
CR pluriharmonic functions
Stability

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10.1016/j.aim.2015.10.002

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abstract = "We give a condition which ensures that the Paneitz operator of an embedded three-dimensional CR manifold is nonnegative and has kernel consisting only of the CR pluriharmonic functions. Our condition requires uniform positivity of the Webster scalar curvature and the stability of the CR pluriharmonic functions for a real analytic deformation. As an application, we show that the real ellipsoids in C2 are such that the CR Paneitz operator is nonnegative with kernel consisting only of the CR pluriharmonic functions.",

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AU - Case, Jeffrey S.

AU - Chanillo, Sagun

AU - Yang, Paul

PY - 2016/1/10

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N2 - We give a condition which ensures that the Paneitz operator of an embedded three-dimensional CR manifold is nonnegative and has kernel consisting only of the CR pluriharmonic functions. Our condition requires uniform positivity of the Webster scalar curvature and the stability of the CR pluriharmonic functions for a real analytic deformation. As an application, we show that the real ellipsoids in C2 are such that the CR Paneitz operator is nonnegative with kernel consisting only of the CR pluriharmonic functions.

AB - We give a condition which ensures that the Paneitz operator of an embedded three-dimensional CR manifold is nonnegative and has kernel consisting only of the CR pluriharmonic functions. Our condition requires uniform positivity of the Webster scalar curvature and the stability of the CR pluriharmonic functions for a real analytic deformation. As an application, we show that the real ellipsoids in C2 are such that the CR Paneitz operator is nonnegative with kernel consisting only of the CR pluriharmonic functions.

KW - CR Paneitz operator

KW - CR pluriharmonic functions

KW - Stability

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EP - 122

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

The CR Paneitz operator and the stability of CR pluriharmonic functions

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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