|
|
Sfb 288 Differential Geometry and Quantum Physics |
Abstract for Sfb Preprint No. 460
Rational minimal surfaces Catherine McCune
In this paper we investigate rational minimal surfaces -- a special class of umbilic-free 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 the transformation used in the iteration and the Darboux-B"acklund transformation for the Korteweg-de Vries equation.
Get a gzip-compressed PostScript copy of this preprint
preprint460.ps.gz (8940 kB)