Singly periodic free boundary minimal surfaces in a solid cylinder of $\mathbb{R}^3$

Abstract

The aim of this work is to show the existence of free boundary minimal surfaces of Saddle Tower type which are embedded in a vertical solid cylinder in $\mathbb{R}^3$ and invariant with respect to a vertical translation. The number of boundary curves equals $2l$, $l \ge 2$.These surfaces come in families depending on one parameter and they converge to $2l$ vertical stripes having a common vertical intersection line.Such surfaces are obtained by perturbing the symmetricallymodified Saddle Tower minimal surfaces.