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

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  • 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 symmetrically modified Saddle Tower minimal surfaces.
    Mathematics Subject Classification: 53A10, 35R35, 53C21.


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