Free boundaries surfaces and Saddle towers minimal surfaces in S-2 x R

Abstract

The aim of this work is to show that for each finite natural number l >= 2 there exists a 1-parameter family of Saddle Tower type minimal surfaces embedded in S-2 x R, invariant with respect to a vertical translation. The genus of the quotient surface is 2l - 1. The proof is based on analytical techniques: precisely we desingularize of the union of gamma(j) x R, j is an element of {1, ... ,2l}, where gamma(j) subset of S-2 denotes a half great circle. These vertical cylinders intersect along a vertical straight line and its antipodal line. As byproduct of the construction we produce free boundary surfaces embedded in (S-2)(+) x R. Such surfaces are extended by reflection in partial derivative(S-2)(+) x R in order to get the minimal surfaces with the desired properties. (c) 2016 Published by Elsevier Inc.