A compactness theorem for the yamabe problem

M. F. Khuri, F. C. Marques, R. M. Schoen

Research output: Contribution to journalArticle

84 Scopus citations

Abstract

In this paper, we prove compactness for the full set of solutions to the Yamabe Problem if n ≥ 24. After proving sharp pointwise estimates at a blowup point, we prove the Weyl Vanishing Theorem in those dimensions, and reduce the compactness question to showing positivity of a quadratic form. We also show that this quadratic form has negative eigenvalues if n ≥ 25.

Original languageEnglish (US)
Pages (from-to)143-196
Number of pages54
JournalJournal of Differential Geometry
Volume81
Issue number1
DOIs
StatePublished - Jan 1 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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