Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the asymptotic Plateau problem for CMC hypersurfaces in hyperbolic
  space   Let $\mathbb{R}_{+}^{n+1}$ \ be the half-space model of the hyperbolic space
$\mathbb{H}^{n+1}.$ It is proved that if $\Gamma\subset\left\{
x_{n+1}=0\right\} \subset\partial_{\infty}\mathbb{H}^{n+1}$ is a bounded
$C^{0}$ Euclidean graph over $\left\{ x_{1}=0,\text{ }x_{n+1}=0\right\} $ then,
given $\left\vert H\right\vert <1,$ there is a complete, properly embedded, CMC
$H$ hypersurface $\Sigma$ of $\mathbb{H}^{n+1}$ such that $\partial_{\infty
}S=\Gamma\cup\left\{ x_{n+1}=+\infty\right\} .$ This result can be seen as a
limit case of the existence theorem proved by B. Guan and J. Spruck in
\cite{GS} on CMC $\left\vert H\right\vert <1$ radial graphs with prescribed
$C^{0}$ asymptotic boundary data.

18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg