Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Every finite graph arises as the singular set of a compact $3$-d
  calibrated area minimizing surface   Given any (not necessarily connected) finite graph in the combinatorial
sense, we construct calibrated 3-dimensional homologically area minimizing
oriented surface on a $7$-dimensional closed compact Riemannian manifold, so
that the singular set of the surface consists of precisely this finite graph.
The constructions are based on some unpublished ideas of Professor Camillo De
Lellis and Professor Robert Bryant.

22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat