Paneitz operator for metrics near S3

Fengbo Hang; Paul C. Yang

doi:10.1007/s00526-017-1201-1

Paneitz operator for metrics near S³

Fengbo Hang, Paul C. Yang

Mathematics

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

Abstract

We derive the first and second variation formula for the Green’s function pole’s value of Paneitz operator on the standard three sphere. In particular it is shown that the first variation vanishes and the second variation is nonpositively definite. Moreover, the second variation vanishes only at the direction of conformal deformation. We also introduce a new invariant of the Paneitz operator and illustrate its close relation with the second eigenvalue and Sobolev inequality of Paneitz operator.

Original language	English (US)
Article number	106
Journal	Calculus of Variations and Partial Differential Equations
Volume	56
Issue number	4
DOIs	https://doi.org/10.1007/s00526-017-1201-1
State	Published - Aug 1 2017

Keywords

58J05
Primary 53A30
Secondary 35J08

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1007/s00526-017-1201-1

Cite this

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abstract = "We derive the first and second variation formula for the Green{\textquoteright}s function pole{\textquoteright}s value of Paneitz operator on the standard three sphere. In particular it is shown that the first variation vanishes and the second variation is nonpositively definite. Moreover, the second variation vanishes only at the direction of conformal deformation. We also introduce a new invariant of the Paneitz operator and illustrate its close relation with the second eigenvalue and Sobolev inequality of Paneitz operator.",

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AB - We derive the first and second variation formula for the Green’s function pole’s value of Paneitz operator on the standard three sphere. In particular it is shown that the first variation vanishes and the second variation is nonpositively definite. Moreover, the second variation vanishes only at the direction of conformal deformation. We also introduce a new invariant of the Paneitz operator and illustrate its close relation with the second eigenvalue and Sobolev inequality of Paneitz operator.

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