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arXiv · 1803.03162

A remark on the rigidity of conformally compact Poincar{é}-Einstein manifolds

Simon Raulot
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Abstract

In this paper, we give an optimal inequality relating the relative Yamabe invariant of a certain compactification of a conformally compact Poin-car{é}-Einstein manifold with the Yamabe invariant of its boundary at infinity. As an application, we obtain an elementary proof of the rigidity of the hyper-bolic space as the only conformally compact Poincar{é}-Einstein manifold with the round sphere as its conformal infinity.

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Simon Raulot. 2018-03-08. A remark on the rigidity of conformally compact Poincar{é}-Einstein manifolds. https://doi.org/10.1007/s11005-018-01146-8

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