Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Free boundary on a cone   We study two phase problems posed over a two dimensional cone generated by a
smooth curve $\gamma$ on the unit sphere. We show that when
$length(\gamma)<2\pi$ the free boundary avoids the vertex of the cone. When
$length(\gamma) \geq 2\pi$ we provide examples of minimizers such that the
vertex belongs to the free boundary.

26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin