A remark on the rigidity of conformally compact Poincaré-Einstein manifolds

Simon Raulot (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

In this paper, we give an optimal inequality relating the relative Yamabe invariant of a certain compactification of a conformally compact Poin-caré-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 Poincaré-Einstein manifold with the round sphere as its conformal infinity.

Domaines: Géométrie différentielle [math.DG]

Simon Raulot. A remark on the rigidity of conformally compact Poincaré-Einstein manifolds. 2018. ⟨hal-01726112⟩