Abstract
Meeks, Pérez 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 a counterexample to this conjecture.
Also, we show that if we consider immersed surfaces instead of embedded ones, then the corresponding statement is true.
Citation
Vanderson Lima. "On a conjecture of Meeks, Pérez and Ros." J. Differential Geom. 125 (3) 613 - 622, November 2023. https://doi.org/10.4310/jdg/1701804152
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