Conformal deformations to scalar-flat metrics with constant mean curvature on the boundary

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Abstract

Let (Mn,g) be a compact manifold with boundary, with finite Sobolev quotient Q(Mn, ∂M). We prove that there exists a conformal deformation which is scalar-flat and has constant boundary mean curvature, if n = 4 or 5 and the boundary is not umbilic. In particular, we prove such existence for any smooth and bounded open set of the Euclidean space, finishing the remaining cases of a theorem of J.F. Escobar.

Original languageEnglish (US)
Pages (from-to)381-405
Number of pages25
JournalCommunications in Analysis and Geometry
Volume15
Issue number2
DOIs
StatePublished - Mar 2007
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Statistics and Probability
  • Geometry and Topology
  • Statistics, Probability and Uncertainty

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