## Abstract

Motivated by the strong maximum principle for the Paneitz operator in dimension 5 or higher found in a preprint by Gursky and Malchiodi and the calculation of the second variation of the Green's function pole's value on S^{3} in our preprint, we study the Riemannian metric on 3-manifolds with positive scalar and Q curvature. Among other things, we show it is always possible to find a constant Q curvature metric in the conformal class. Moreover, the Green's function is always negative away from the pole, and the pole's value vanishes if and only if the Riemannian manifold is conformal diffeomorphic to the standard S^{3}. Compactness of constant Q curvature metrics in a conformal class and the associated Sobolev inequality are also discussed.

Original language | English (US) |
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Pages (from-to) | 734-744 |

Number of pages | 11 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 69 |

Issue number | 4 |

DOIs | |

State | Published - Apr 1 2016 |

## ASJC Scopus subject areas

- General Mathematics
- Applied Mathematics