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Computational Methods and Function Theory

, Volume 9, Issue 2, pp 609–632 | Cite as

On Riemann-Hilbert Problems in Circle Packing

  • Elias Wegert
  • David Bauer
Article

Abstract

We propose a discrete counterpart of non-linear boundary value problems for holomorphic functions (Riemann-Hilbert problems) in the framework of circle packing. For packings with simple combinatorial structure and circular target curves appropriate solvability conditions are given and the set of all solutions is described. We compare the discrete and the continuous setting and discuss several discretization effects. In the last section we indicate promising directions for further research and report on the results of some test calculations which show that solutions of the circle packing problem approximate the classical solutions surprisingly well.

Keywords

Riemann-Hilbert problems circle packing conformal geometry hyperbolic geometry 

2000 MSC

Primary 30E25 Secondary 52C26 30C35 kl]30C80 

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Copyright information

© Heldermann  Verlag 2009

Authors and Affiliations

  1. 1.Institute of Applied AnalysisTech Univ Bergakademie FreibergFreibergGermany
  2. 2.MPI for Mathematics in the SciencesLeipzigGermany

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