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

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.

References in corpus (2)

• Unique continuation results for Ricci curvature and applications
• Non-singular spacetimes with a negative cosmological constant: II. Static solutions of the Einstein-Maxwell equations

Cited by in corpus (1)

• Scalar Flat Compactifications Of Poincar{é}-einstein Manifolds And Applications