Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The size of isoperimetric surfaces in 3-manifolds and a rigidity result
  for the upper hemisphere   We characterize the standard $\mathbb{S}^3$ as the closed Ricci-positive
3-manifold with scalar curvature at least 6 having isoperimetric surfaces of
largest area: $4\pi$. As a corollary we answer in the affirmative an
interesting special case of a conjecture of Min-Oo's on the scalar curvature
rigidity of the upper hemisphere..

33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess