Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Limiting case Hardy inequalities on the sphere   We give sharp limiting case Hardy inequalities on the sphere $\mathbb{S}^{2}$
and show that their optimal constants are unattainable by any $f\in
H^{1}\left(\mathbb{S}^{2}\right)\setminus\{0\}$. The singularity of the problem
is related to the geodesic distance from a point on the sphere.

25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph