
A note on balance equations for doubly periodic minimal surfacesA note on balance equations for doubly periodic minimal surfacesAA00723502 
"/Connor, Peter/"Connor, Peter
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130 , 201701 , Department of Mathematics, Faculty of Science, Okayama University
ISSN:00301566
NCID:AA00723502
Description
Most known examples of doubly periodic minimal surfaces in R<sup>3</sup> with parallel ends limit as a foliation of R<sup>3</sup> 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 threeparameter 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.
FullText
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