Conformal Metrics with Prescribed Fractional Scalar Curvature on Conformal Infinities with Positive Fractional Yamabe Constants

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Abstract

Let (X, g+) be an asymptotically hyperbolic manifold with conformal infinity (M, [h^]). Our primary aim is to introduce the prescribed fractional scalar curvature problem on M and to provide its solutions under various geometric conditions on X and M. We also deduce the existence results for the fractional Yamabe problem in the end-point cases, e.g., n= 3 , γ=12 and M is non-umbilic, etc. Finally, we prove that all solutions we find here are smooth on M.

Original languageEnglish
Pages (from-to)4287-4327
Number of pages41
JournalJournal of Geometric Analysis
Volume31
Issue number4
DOIs
StatePublished - 2021 Apr

Keywords

  • Existence
  • Fractional Yamabe problem
  • Prescribed fractional scalar curvature problem
  • Regularity

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