Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ricci curvature, minimal surfaces and sphere theorems   Using an analogue of Myers' theorem for minimal surfaces and three
dimensional topology, we prove the diameter sphere theorem for Ricci curvature
in dimension three and a corresponding eigenvalue pinching theorem. This
settles these two open problems for closed 3 manifolds with positive Ricci
curvature since they are both false in dimensions greater than three.

31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph