Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A variational proof for the existence of a conformal metric with
  preassigned negative Gaussian curvature for compact Riemann surfaces of genus
  $>1$   Given an smooth function $K <0$ we prove a result by Berger, Kazhdan and
others that in every conformal class there exists a metric which attains this
function as its Gaussian curvature for a compact Riemann surface of genus
$g>1$. We do so by minimizing an appropriate functional using elementary
analysis. In particular for $K$ a negative constant, this provides an
elementary proof of the uniformization theorem for compact Riemann surfaces of
genus $g >1$.

29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin