Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Plateau-Douglas problem for singular configurations and in general
  metric spaces   Assume you are given a finite configuration $\Gamma$ of disjoint rectifiable
Jordan curves in $\mathbb{R}^n$. The Plateau-Douglas problem asks whether there
exists a minimizer of area among all compact surfaces of genus at most $p$
which span $\Gamma$. While the solution to this problem is well-known, the
classical approaches break down if one allows for singular configurations
$\Gamma$ where the curves are potentially non-disjoint or self-intersecting.
Our main result solves the Plateau-Douglas problem for such potentially
singular configurations. Moreover, our proof works not only in $\mathbb{R}^n$
but in general proper metric spaces. Thus we are also able to extend previously
known existence results of J\"urgen Jost as well as of the second author
together with Stefan Wenger for regular configurations. In particular,
existence is new for disjoint configurations of Jordan curves in general
complete Riemannian manifolds. A minimal surface of fixed genus $p$ bounding a
given configuration $\Gamma$ need not always exist, even in the most regular
settings. Concerning this problem, we also generalize the approach for singular
configurations via minimal sequences satisfying conditions of cohesion and
adhesion to the setting of metric spaces.

22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th