Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inverse Scattering on Asymptotically Hyperbolic Manifolds   Scattering is defined on compact manifolds with boundary which are equipped
with an asymptotically hyperbolic metric, $g.$ A model form is established for
such metrics close to the boundary. It is shown that the scattering matrix at
energy $\zeta$ exists and is a pseudo-differential operator of order $2\zeta+1
- \dim X.$ The symbol of the scattering matrix is then used to show that except
for a countable set of energies the scattering matrix at one energy determines
the diffeomorphism class of the metric modulo terms vanishing to infinite order
at the boundary. An analogous result is proved for potential scattering. The
total symbol is computed when the manifold is hyperbolic or is of product type
modulo terms vanishing to infinite order at the boundary. The same methods are
then applied to studying inverse scattering on the Schwarzschild and De
Sitter-Schwarzschild models of black holes.

18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int