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arXiv · 1103.1340

Immersed solutions of Plateau's problem for piecewise smooth boundary curves with small total curvature

Laura Desideri·Ruben Jakob
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Abstract

We provide a new proof of the classical result that any closed rectifiable Jordan curve Gamma in space being piecewise of class C^2 bounds at least one immersed minimal surface of disc-type, under the additional assumption that the total curvature of Gamma is smaller than 6*Pi. In contrast to the methods due to Osserman, Gulliver and Alt, our proof relies on a polygonal approximation technique, using the existence of immersed solutions of Plateau's problem for polygonal boundary curves, provided by the first author's accomplishment of Garnier's ideas.

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Laura Desideri, Ruben Jakob. 2012-02-28. Immersed solutions of Plateau's problem for piecewise smooth boundary curves with small total curvature. https://arxiv.org/abs/1103.1340

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