2012/01/18 by Mehdi Belraouti, Belraouti, Mehdi
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG
paper · pdf · doi:10.48550/arxiv.1201.3716
arxiv created 2012/01/18 · arxiv updated 2012/01/19
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 \citeMR1857817. 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.