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 + Show 1 more

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https://doi.org/10.1016/j.aim.2015.10.002

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Journal: Advances in Mathematics	Publication Date: Nov 20, 2015
Citations: 14	License type: publisher-specific-oa

Affiliation: Rutgers, The State University of New Jersey, Princeton University

#CR Paneitz Operator #Real Ellipsoids + Show 8 more

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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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