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arXiv · 1809.05593

Compactness of conformally compact Einstein manifolds in dimension 4

Sun-Yung A. Chang·Yuxin Ge
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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.

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Sun-Yung A. Chang, Yuxin Ge. 2018-09-14. Compactness of conformally compact Einstein manifolds in dimension 4. https://arxiv.org/abs/1809.05593

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