Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic behavior of Cauchy hypersurfaces in constant curvature
  space-times   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.

30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th