Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Geodesic distance for right-invariant metrics on diffeomorphism groups:
  critical Sobolev exponents
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ