Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The problem of prescribed critical functions   Let $(M,g)$ be a compact Riemannian manifold on dimension $n \geq 4$ not
conformally diffeomorphic to the sphere $S^n$. We prove that a smooth function
$f$ on $M$ is a critical function for a metric $\tilde{g}$ conformal to $g$ if
and only if there exists $x \in M$ such that $f(x)>0$.

25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys