Compactness of conformally compact Einstein manifolds in dimension 4

Published 14 Sep 2018 in math.DG | (1809.05593v2)

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.

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