Sur la géométrie de la singularité initiale des espaces-temps plats globalement hyperboliques

Abstract

Let $M$ be a maximal globally hyperbolic Cauchy compact flat spacetime of dimension 2+1, admitting a Cauchy hypersurface diffeomorphic to a compact hyperbolic manifold. We study the asymptotic behaviour of level sets of quasi-concave time functions on $M$. We give a positive answer to a conjecture of Benedetti and Guadagnini in \cite{MR1857817}. More precisely, we prove that the level sets of such a time function converge in the Hausdorff-Gromov equivariant topology to a real tree. Moreover, this limit does not depend on the choice of the time function.

References in corpus (2)

• Globally Hyperbolic Flat Spacetimes
• Sur la compactification de Thurston de l'espace de Teichmüller

Cited by in corpus (1)

• On the Weyl problem for complete surfaces in the hyperbolic and anti-de Sitter spaces