Rational minimal surfaces
Abstract (Summary)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-BÃ?Â¤cklund transformation for the Korteweg-de Vries equation.
School Location:USA - Massachusetts
Source Type:Master's Thesis
Date of Publication:01/01/1999