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On the topology of conformally compact Einstein 4-manifolds

Alice Chang·Jie Qing·Paul Yang
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Abstract

In this paper we study the topology of conformally compact Einstein 4-manifolds. When the conformal infinity has positive Yamabe invariant and the renormalized volume is also positive we show that the conformally compact Einstein 4-manifold will have at most finite fundamental group. Under the further assumption that the renormalized volume is relatively large, we conclude that the conformally compact Einstein 4-manifold is diffeomorphic to $B^4$ and its conformal infinity is diffeomorphic to $S^3$.

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Alice Chang, Jie Qing, Paul Yang. 2003-05-23. On the topology of conformally compact Einstein 4-manifolds. https://arxiv.org/abs/math/0305085

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