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arXiv · 1806.03883

On a conjecture of Meeks, P\'erez and Ros

Vanderson Lima
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Abstract

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.

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Vanderson Lima. 2018-06-11. On a conjecture of Meeks, P\'erez and Ros. https://arxiv.org/abs/1806.03883

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