Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generic Transversality of Minimal Submanifolds and Generic Regularity of
  Two-Dimensional Area-Minimizing Integral Currents   Suppose that $N$ is a smooth manifold with a smooth Riemannian metric $g_0$,
and that $\Gamma$ is a smooth submanifold of $N$. This paper proves that for a
generic (in the sense of Baire category) smooth metric $g$ conformal to $g_0$,
if $F$ is any simple $g$-minimal immersion of a closed manifold into N, then
$F$ is transverse to $\Gamma$ and $F$ is self-transverse. The theorem remains
true with "transverse" and "self-transverse" replaced by "strongly transverse"
and "strongly self-transverse". The theorem also holds for hypersurfaces of
constant mean curvature or, more generally, of prescribed mean curvature.
  The paper also proves that for a generic ambient metric, every
$2$-dimensional surface (integral current or flat chain mod $2$) without
boundary that minimizes area in its homology class has support equal to a
smoothly embedded minimal surface.

33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat