SINGLY PERIODIC FREE BOUNDARY MINIMAL SURFACES IN A SOLID CYLINDER OF 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 R-3 and invariant with respect to a vertical translation. The number of boundary curves equals 2l, l >= 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.