Paneitz operator for metrics near S3

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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 languageEnglish (US)
Article number106
JournalCalculus of Variations and Partial Differential Equations
Volume56
Issue number4
DOIs
StatePublished - Aug 1 2017

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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