Existence results for the Yamabe problem on manifolds with boundary

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Abstract

Given a compact Riemannian manifold with umbilic boundary, we prove the existence of conformally related metrics of zero scalar curvature and constant mean curvature on the boundary, under suitable hypotheses on the Weyl tensor. In order to carry out the estimates on the Sobolev quotient, we also prove the existence of conformal Fermi coordinates.

Original languageEnglish (US)
Pages (from-to)1599-1620
Number of pages22
JournalIndiana University Mathematics Journal
Volume54
Issue number6
DOIs
StatePublished - Jan 1 2005
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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