Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Liouville theorem, conformally invariant cones and umbilical surfaces
  for Grushin-type metrics   We prove a classification theorem for conformal maps with respect to the
control distance generated by a system of diagonal vector fields.
  It turns out that all such maps can be obtained as compositions of suitable
dilations, inversions and isometries. We also classify all umbilical surfaces
of the underlying metric.

34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat