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Minimal surfaces in a wedge I. Asymptotic expansions

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Abstract

In this paper we investigate the boundary behaviour of minimal surfaces in a wedge which are either of class ℐ (Γ, ℱ) or of class ℰ(Γ, ℱ) Here Γ denotes a Jordan curve in ℝ 3 whose endpoints lie on a support surface ℱ which is assumed to be the boundary of a wedge. Then, roughly speaking, ℐ (Γ, ℱ) denotes the set of disk-type minimal surfaces which are stationary in 〈 Γ, ℐ 〉 and whose free traces on ℱ intersect the edge ℒ of the wedge “trans versally”, while ℰ(Γ, ℱ) denotes the class of corresponding surfaces whose free traces attach to ℒ in full intervals. We derive asymptotic expansions of X w and N w where X(w), w ≠ B, is a minimal surface of class ℐ(Γ, ℱ) or ℰ(Γ, ℱ), and N(w) denotes the Gauss map corresponding to X.

In forthcoming papers we plan to investigate existence and uniqueness questions for minimal surfaces in a wedge.

We would like to thank Gudrun Turowski for carefully reading our manuscript and for critical remarks.

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References

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Authors and Affiliations

  1. Mathematisches Institut der Universität Bonn, Beringstraße 1, D-53115, Bonn, Germany

    Stefan Hildebrandt

  2. Institut für Mathematik der Brandenburgischen Technischen Universität, Postfach 101344, D-03013, Cottbus, Germany

    Friedrich Sauvigny

Authors
  1. Stefan Hildebrandt
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  2. Friedrich Sauvigny
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Dedicated to Professor Rolf Lets on occasion of his 65th birthday

This article was processed by the authors using the LATEX style file pljourlm from Springer-Verlag.

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Hildebrandt, S., Sauvigny, F. Minimal surfaces in a wedge I. Asymptotic expansions. Calc. Var. 5, 99–115 (1997). https://doi.org/10.1007/s005260050061

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  • DOI: https://doi.org/10.1007/s005260050061

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