Solving period problems for minimal surfaces with the support function

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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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Differential Geometry, 53A10

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http://salesiana.dossiersoluciones.com/handle/123456789/163621

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0806.4179
 http://arxiv.org/abs/0806.4179

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arXiv