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

Filippo Morabito

doi:10.3934/dcds.2015.35.4987

Article Contents

2015, Volume 35, Issue 10: 4987-5001. Doi: 10.3934/dcds.2015.35.4987

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

Filippo Morabito^1,

1.
KAIST, Department of Mathematical Sciences, 291 Daehak-ro, Yuseong-gu, Daejeon, 305-701

Received: August 2014

Revised: February 2015

Published: October 2015

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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 symmetrically modified Saddle Tower minimal surfaces.

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Mathematics Subject Classification: 53A10, 35R35, 53C21.

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References

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