# Paneitz operator for metrics near S-3

## Author(s): Hang, Fengbo; Yang, Paul C.

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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. Publication Date: Aug-2017 Electronic Publication Date: 10-Jul-2017 Citation: Hang, Fengbo, Yang, Paul C. (2017). Paneitz operator for metrics near S-3. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 56, doi:10.1007/s00526-017-1201-1 DOI: doi:10.1007/s00526-017-1201-1 ISSN: 0944-2669 EISSN: 1432-0835 Pages: 1 - 25 Type of Material: Journal Article Journal/Proceeding Title: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS Version: Author's manuscript