Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A spherical Bernstein theorem for minimal submanifolds of higher
  codimension   Combining the tools of geometric analysis with properties of Jordan angles
and angle space distributions, we derive a spherical and a Euclidean Bernstein
theorem for minimal submanifolds of arbitrary dimension and codimension, under
the condition that the Gauss image is contained in some geometrically defined
closed region of a Grassmannian manifold. The proof depends on the
subharmoncity of an auxiliary function, the Codazzi equations and geometric
measure theory.

7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph