Abstract
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 H2×R,H2 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.
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