Mathematical Journal of Okayama University 59巻 1号
2017-01 発行

A note on balance equations for doubly periodic minimal surfaces

Connor, Peter Department of Mathematical Sciences, Indiana University South Bend
Publication Date
2017-01
Abstract
Most known examples of doubly periodic minimal surfaces in R3 with parallel ends limit as a foliation of R3 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