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.
All Science Journal Classification (ASJC) codes
- Conformally compact Einstein manifolds
- Fefferman–Graham compactification