On a conjecture of Meeks, P\'erez and Ros
Differential Geometry
2021-07-14 v3 Geometric Topology
Abstract
Meeks, P\'erez and Ros conjectured that a closed Riemannian -manifold which does not admit any closed embedded minimal surface whose two-sided covering is stable, must be diffeomorphic to a quotient of the -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.
Cite
@article{arxiv.1806.03883,
title = {On a conjecture of Meeks, P\'erez and Ros},
author = {Vanderson Lima},
journal= {arXiv preprint arXiv:1806.03883},
year = {2021}
}
Comments
Final version. Accepted for publication in Journal of Differential Geometry