Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a conjecture of Meeks, P\'erez and Ros   Meeks, P\'erez and Ros conjectured that a closed Riemannian $3$-manifold
which does not admit any closed embedded minimal surface whose two-sided
covering is stable, must be diffeomorphic to a quotient of the $3$-sphere. We
give an counterexample to this conjecture. Also, we show that if we consider
immersed surfaces instead of embedded ones, then the corresponding statement is
true.

14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org