Singly periodic free boundary minimal surfaces in a solid cylinder of H^2 x R

The aim of this work is to show there exist free boundary minimal surfaces of Saddle Tower type which are embedded in a vertical solid cylinder of H^2×R, H^2 being the hyperbolic plane, and invariant under the action of a vertical translation and a rotation. 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 intersection line.