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Abstract
In this article the author firstly gives a short overview over the results which have been achieved so far concerning the question which boundary contours in ℝ3 can bound only finitely many (stable) immersed minimal surfaces. After that the author describes the course of the proof of his result in [22], which states that a simple closed polygon in ℝ3 can bound only finitely many immersed minimal surfaces of disc-type if it meets the following two requirements: firstly it has to bound only minimal surfaces without boundary branch points, and secondly its total curvature, i.e. the sum of the exterior angles at its vertices, has to be smaller than 6π.
Keywords: finiteness of the set of solutions; Plateaus problem for polygonal boundary curves. MSC classification: 49Q05.
Published Online: 2009-12-04
Published in Print: 2009-11
© by Oldenbourg Wissenschaftsverlag, München, Germany
