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Minimal Surfaces from Circle Patterns: Boundary Value Problems, Examples

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Discrete Differential Geometry

Part of the book series: Oberwolfach Seminars ((OWS,volume 38))

Abstract

We construct discrete solutions to a class of boundary value problems for minimal surfaces without ends, including special classes of Plateau’s problem. The boundary consists of finitely many straight line segments lying on the surface and/or planes intersecting the surface orthogonally. The discrete minimal surfaces which satisfy the given boundary conditions are built from a combinatorial parametrization, using an orthogonal circle pattern which approximates the Gauss map and a discrete duality transformation for S-isothermic surfaces.

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References

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Authors and Affiliations

  1. Institut für Mathematik, MA 8-3, Technische Universität Berlin, Str. des 17. Juni 136, 10623, Berlin, Germany

    Ulrike Bücking

Authors
  1. Ulrike Bücking
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Editor information

Editors and Affiliations

  1. Institut für Mathematik, MA 8-3, Technische Universität Berlin, Strasse des 17. Juni 136, 10623, Berlin, Germany

    Alexander I. Bobenko

  2. Institut für Mathematik, MA 3-2, Technische Universität Berlin, Strasse des 17. Juni 136, 10623, Berlin, Germany

    John M. Sullivan

  3. Department of Computer Science, Caltech, MS 256-80, 1200 E. California Blvd., Pasadena, CA, 91125, USA

    Peter Schröder

  4. Institut für Mathematik, MA 6-2, Technische Universität Berlin, Strasse des 17. Juni 136, 10623, Berlin, Germany

    Günter M. Ziegler

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© 2008 Birkhäuser Verlag Basel/Switzerland

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Bücking, U. (2008). Minimal Surfaces from Circle Patterns: Boundary Value Problems, Examples. In: Bobenko, A.I., Sullivan, J.M., Schröder, P., Ziegler, G.M. (eds) Discrete Differential Geometry. Oberwolfach Seminars, vol 38. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8621-4_2

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