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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.|
|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|
|Pages:||1 - 25|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS|
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