Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A prescribed scalar and boundary mean curvature problem on compact
  manifolds with boundary   We consider the problem of finding a metric in a given conformal class with
prescribed nonpositive scalar curvature and nonpositive boundary mean curvature
on a compact manifold with boundary, and establish a necessary and sufficient
condition in terms of a conformal invariant that measures the zero set of the
target curvatures.

21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn