Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Sobolev and isoperimetric inequalities for submanifolds in weighted
  ambient spaces
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci