Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Sharp Hardy inequalities in an exterior of a ball
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th