Compactness of conformally compact Einstein 4-manifolds II

Abstract

In this paper, we establish a number of compactness results for some class of conformally compact Einstein 4-manifolds. In the first part of the paper, we improve the earlier compactness results obtained by Chang-Ge [15]. In the second part of the paper, as applications, we derive some further compactness results under the perturbation condition when the L2 norm of the Weyl curvature is small. We also derive the global uniqueness of conformally compact Einstein metrics on the 4-Ball constructed in the earlier work of Graham-Lee [31].