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On compactness conformally compact Einstein manifolds and uniqueness of Graham-Lee metrics, III (2107.03075v1)
Published 7 Jul 2021 in math.DG
Abstract: In this paper, we establish a compactness result for a class of conformally compact Einstein metrics defined on manifolds of dimension $d\ge 4$. As an application, we derive the global uniqueness of a class of conformally compact Einstein metric defined on the $d$-dimensional ball constructed in the earlier work of Graham-Lee with $d\ge 4$. As a second application, we establish some gap phenomenon for a class of conformal invariants.