On the topology of conformally compact Einstein 4-manifolds

Details On the topology of conformally compact Einstein 4-manifolds On the topology of conformally compact Einstein 4-manifolds

2003-05-06

arxiv.org/abs/math/0305085v2

Mathematics

Differential Geometry

16 pages

Scientific paper

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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