Paneitz operator for metrics near $$S^{3}$$ S 3

2017 ◽  
Vol 56 (4) ◽  
Author(s):  
Fengbo Hang ◽  
Paul C. Yang
Keyword(s):  
Paneitz Operator

scholarly journals The CR Paneitz operator and the stability of CR pluriharmonic functions

2016 ◽  
Vol 287 ◽  
pp. 109-122 ◽  
Author(s):  
Jeffrey S. Case ◽  
Sagun Chanillo ◽  
Paul Yang
Keyword(s):  
Paneitz Operator ◽  
Pluriharmonic Functions ◽  
The Stability

scholarly journals A remark on the kernel of the CR Paneitz operator

2015 ◽  
Vol 126 ◽  
pp. 153-158 ◽  
Author(s):  
Jeffrey S. Case ◽  
Sagun Chanillo ◽  
Paul Yang
Keyword(s):  
Paneitz Operator

scholarly journals AN OBATA-TYPE THEOREM ON A THREE-DIMENSIONAL CR MANIFOLD

2013 ◽  
Vol 56 (2) ◽  
pp. 283-294 ◽  
Author(s):  
S. IVANOV ◽  
D. VASSILEV
Keyword(s):  
Unit Sphere ◽  
Type Theorem ◽  
Three Dimensional ◽  
First Eigenvalue ◽  
Dimensional Manifold ◽  
Type Condition ◽  
Cr Manifold ◽  
The First Eigenvalue ◽  
Paneitz Operator ◽  
Dimensional Unit

AbstractWe prove the CR version of the Obata's result for the first eigenvalue of the sub-Laplacian in the setting of a compact strictly pseudoconvex pseudohermitian three-dimensional manifold with non-negative CR-Paneitz operator which satisfies a Lichnerowicz-type condition. We show that if the first positive eigenvalue of the sub-Laplacian takes the smallest possible value, then, up to a homothety of the pseudohermitian structure, the manifold is the standard Sasakian three-dimensional unit sphere.

scholarly journals Estimates for eigenvalues of the Paneitz operator

2014 ◽  
Vol 257 (10) ◽  
pp. 3868-3886 ◽  
Author(s):  
Qing-Ming Cheng
Keyword(s):  
Paneitz Operator

scholarly journals A Perturbation Approach for Paneitz Energy on Standard Three Sphere

2018 ◽  
Vol 2020 (11) ◽  
pp. 3295-3317
Author(s):  
Fengbo Hang ◽  
Paul C Yang
Keyword(s):  
Variational Problems ◽  
Higher Order ◽  
Sharp Inequality ◽  
Perturbation Approach ◽  
Yamabe Problem ◽  
Extremal Functions ◽  
Three Sphere ◽  
Paneitz Operator

Abstract We present another proof of the sharp inequality for Paneitz operator on the standard three sphere, in the spirit of subcritical approximation for the classical Yamabe problem. To solve the perturbed problem, we use a symmetrization process which only works for extremal functions. This gives a new example of symmetrization for higher-order variational problems.

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