Rational minimal surfaces

In this thesis we investigate rational minimal surfaces—a special class of minimal surfaces with finite total curvature and Enneper type ends. We define an iteration for Gauss maps and show that it can be used to produce infinitely many families of rational functions that yield rational minimal surfaces—the Schwarzian derivative plays an important role in the proof. We also investigate a relationship between dualization, as defined in the iteration, and the Darboux-Bäcklund transformation for the Korteweg-de Vries equation