2015/03/21 by Mehdi Belraouti, Belraouti, Mehdi · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Holomorphic and Operator Theory #Mathematical Dynamics and Fractals #math.DG
paper · pdf · doi:10.48550/arxiv.1503.06343
arxiv created 2015/03/21 · openalex publication_date 2015/03/21 · arxiv updated 2015/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the asymptotic behavior of convex Cauchy hypersurfaces on maximal globally hyperbolic spatially compact space-times of constant curvature. We generalise the result of [11] to the (2+1) de Sitter and anti de Sitter cases. We prove that in these cases the level sets of quasi-concave times converge in the Gromov equivariant topology, when time goes to 0, to a real tree. Moreover, this limit does not depend on the choice of the time function. We also consider the problem of asymptotic behavior in the flat (n+1) dimensional case. We prove that the level sets of quasi-concave times converge in the Gromov equivariant topology, when time goes to 0, to a CAT (0) metric space. Moreover, this limit does not depend on the choice of the time function.