A priori estimates for the yamabe problem in the non-locally conformally flat case

Research output: Contribution to journalArticle

65 Scopus citations

Abstract

Given a compact Riemannian manifold (Mn, g), with positive Yamabe quotient, not conformally diffeomorphic to the standard sphere, we prove a priori estimates for solutions to the Yamabe problem. We restrict ourselves to the dimensions where the Positive Mass Theorem is known to be true, that is, when n ≤ 7. We also show that, when n ≥ 6, the Weyl tensor has to vanish at a point where solutions to the Yamabe equation blow up.

Original languageEnglish (US)
Pages (from-to)315-346
Number of pages32
JournalJournal of Differential Geometry
Volume71
Issue number2
DOIs
StatePublished - Jan 1 2005
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

Fingerprint Dive into the research topics of 'A priori estimates for the yamabe problem in the non-locally conformally flat case'. Together they form a unique fingerprint.

  • Cite this