Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A two-piece property for free boundary minimal hypersurfaces in the
  $(n+1)$-dimensional ball   We prove that every hyperplane passing through the origin in $\rr^{n+1}$
divides an embedded compact free boundary minimal hypersurface of the euclidean
$(n+1)$-ball in exactly two connected hypersurfaces. We also show that if a
region in the $(n+1)$-ball has mean convex boundary and contains a
nullhomologous $(n-1)$-dimensional equatorial disk, then this region is a
closed halfball. Our first result gives evidence to a conjecture by Fraser and
Li in any dimension.

25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc