### Abstract

Original language | Undefined |
---|---|

Article number | 1504.02032 |

Journal | arXiv |

State | Published - Apr 8 2015 |

### Keywords

- math.DG
- math.AP
- 58J05, 53C21

### Cite this

**Paneitz operator for metrics near S ^{3}.** / Hang, Fengbo; Yang, Paul C.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Paneitz operator for metrics near S3

AU - Hang, Fengbo

AU - Yang, Paul C.

N1 - 25 pages

PY - 2015/4/8

Y1 - 2015/4/8

N2 - 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.

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.

KW - math.DG

KW - math.AP

KW - 58J05, 53C21

M3 - Article

JO - arXiv

JF - arXiv

M1 - 1504.02032

ER -