Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Area rigidity for the equatorial disk in the ball   It is proved by Brendle in [4] that the equatorial disk $D^k$ has least area
among $k$-dimensional free boundary minimal surfaces in the Euclidean ball
$B^n$. By comparing the excess of free boundary minimal surfaces with the
excess of the associated cones over the boundary, we prove the existence of a
gap for the area.

17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int