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

Mehdi Belraouti (1)

1 LANLG - Laboratoire d'Analyse non linéaire et Géométrie

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.

Domaines: Géométrie différentielle [math.DG]

Mehdi Belraouti. Sur la géométrie de la singularité initiale des espaces-temps plats globalement hyperboliques. 2011. ⟨hal-00633198v3⟩