Rigidity of conformal boundaries in pseudo-Riemannian geometry

A convenient way to build a conformal boundary to a (noncompact) pseudo-Riemannian manifold (M, g), is to embed conformally (M, g) as a strict open subset of a manifold (N, h) of the same dimension, and then consider the topological boundary of the embedding. The aim of the talk is to discuss the possibility of such a strict embedding, and then to show that as soon as we deal with manifolds of dimension _ 3, $the conformal boundary essentially does not depend on the embedding.$ $We will also generalize this rigidity property of boundaries to other geometric structures.$