Compactness of conformally compact Einstein manifolds in dimension 4

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Abstract

In this paper, we establish some compactness results of conformally compact Einstein metrics on 4-dimensional manifolds. Our results were proved under assumptions on the behavior of some local and non-local conformal invariants, on the compactness of the boundary metrics at the conformal infinity, and on the topology of the manifolds.

Original languageEnglish (US)
Pages (from-to)588-652
Number of pages65
JournalAdvances in Mathematics
Volume340
DOIs
StatePublished - Dec 15 2018

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Conformally compact Einstein manifolds
  • Fefferman–Graham compactification
  • Q-curvature
  • S-tensor

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