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arXiv · 2208.14998

Free boundary minimal annuli immersed in the unit ball

Isabel Fernandez·Laurent Hauswirth·Pablo Mira
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Abstract

We construct a family of compact free boundary minimal annuli immersed in the unit ball $\mathbb{B}^3$ of $\mathbb{R}^3$, the first such examples other than the critical catenoid. This solves a problem formulated by Nitsche in 1985. These annuli are symmetric with respect to two orthogonal planes and a finite group of rotations around an axis, and are foliated by spherical curvature lines. We show that the only free boundary minimal annulus embedded in $\mathbb{B}^3$ foliated by spherical curvature lines is the critical catenoid; in particular, the minimal annuli that we construct are not embedded. On the other hand, we also construct families of non-rotational compact embedded capillary minimal annuli in $\mathbb{B}^3$. Their existence solves in the negative a problem proposed by Wente in 1995.

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Isabel Fernandez, Laurent Hauswirth, Pablo Mira. 2022-11-08. Free boundary minimal annuli immersed in the unit ball. https://arxiv.org/abs/2208.14998

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