Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of Minimizers for the Reifenberg Plateau problem   That is, given a compact set $B \subset \mathbb{R}^n$ (the boundary) and a
subgroup $L$ of the \v{C}ech homology group $\check{H}_{d-1}(B;G)$ of dimension
$d$ over some commutative group $G$, we find a compact set $E \supset B$ such
that the image of $L$ by the natural map
$\check{H}_{d-1}(B;G)\to\check{H}_{d-1}(S;G)$ induced by the inclusion $B \to
E$, is reduced to $\{ 0 \}$, and such that the Hausdorff measure
$\mathcal{H}^{d}(E \setminus B)$ is minimal under these constraints. Thus we
have no restriction on the group $G$ or the dimensions $0 < d < n$.

31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th