Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The periodic Plateau problem and its application   Given a noncompact disconnected complete periodic curve $\Gamma$ with no self
intersection in $\mathbb R^3$, it is proved that there exists a noncompact
simply connected periodic minimal surface spanning $\Gamma$. As an application
it is shown that for any tetrahedron $T$ with dihedral angles $\leq90^\circ$
there exist four embedded minimal annuli in $T$ which are perpendicular to
$\partial T$ along their boundary. It is also proved that every Platonic solid
of $\mathbb R^3$ contains five types of free boundary embedded minimal surfaces
of genus zero.

17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess