Q Curvature on a Class of 3-Manifolds

Fengbo Hang, Paul C. Yang

Research output: Contribution to journalArticlepeer-review

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 S3 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 S3. Compactness of constant Q curvature metrics in a conformal class and the associated Sobolev inequality are also discussed.

Original languageEnglish (US)
Pages (from-to)734-744
Number of pages11
JournalCommunications on Pure and Applied Mathematics
Volume69
Issue number4
DOIs
StatePublished - Apr 1 2016

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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