Mathematical Journal of Okayama University 59巻 1号

2017-01 発行

Connor, Peter
Department of Mathematical Sciences, Indiana University South Bend

Publication Date

2017-01

Abstract

Most known examples of doubly periodic minimal surfaces in R^{3} with parallel ends limit as a foliation of R^{3} by horizontal noded planes, with the location of the nodes satisfying a set of balance equations. Conversely, for each set of points providing a balanced configuration, there is a corresponding three-parameter family of doubly periodic minimal surfaces. In this note we derive a differential equation that is equivalent to the balance equations for doubly periodic minimal surfaces. This allows for the generation of many more solutions to the balance equations, enabling the construction of increasingly complicated surfaces.

Keywords

minimal surfaces

doubly periodic

balance equations