Paneitz operator for metrics near \(S^{3}\)

  • Fengbo HangEmail author
  • Paul C. Yang


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.

Mathematics Subject Classification

Primary 53A30 Secondary 35J08 58J05 



We would like to thank the refree for his/her careful reading of the article and many comments that improved the presentation of the paper. The research of Yang is supported by NSF Grant DMS 1104536 and 1509505.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Courant InstituteNew York UniversityNew YorkUSA
  2. 2.Department of MathematicsPrinceton UniversityPrincetonUSA

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