Solving period problems for minimal surfaces with the support function

Details Solving period problems for minimal surfaces with the support function Solving period problems for minimal surfaces with the support function

2008-06-25

arxiv.org/abs/0806.4179v1

Mathematics

Differential Geometry

Scientific paper

In this paper we show how to bypass the usual difficulties in the analysis of elliptic integrals that arise when solving period problems for minimal surfaces. The method consists of replacing period problems with ordinary Sturm-Liouville problems involving the support function. We give a practical application by proving existence of the sheared Scherk-Karcher family of surfaces numerically described by Wei. Moreover, we show that this family is continuous, and both of its limit-members are the singly periodic genus-one helicoid.

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