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Circle packing with generalized branching

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Abstract

There is a fairly comprehensive theory of discrete analytic functions based on circle packing. In this theory, discrete analytic functions are represented as maps between circle packings that share combinatorial tangency patterns. Branching behavior, however, has until now been restricted by the need to place branch points at circle centers. In this paper, the authors introduce mechanisms for generalized branching which remove this restriction. Their use is illustrated by overcoming combinatorial obstructions to branching in the construction of a discrete Ahlfors function.

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Authors and Affiliations

  1. University of Tennessee, Knoxville, TN, USA

    Kenneth Stephenson

  2. Western Governors University, Salt Lake, USA

    James Ashe

  3. Heilbronn Institute of Mathematical Research, University of Bristol , Bristol, UK

    Edward Crane

Authors
  1. James Ashe
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  2. Edward Crane
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  3. Kenneth Stephenson
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Correspondence to Kenneth Stephenson.

Additional information

Dedicated to C. David Minda on the occasion of his retirement.

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Ashe, J., Crane, E. & Stephenson, K. Circle packing with generalized branching. J Anal 24, 251–276 (2016). https://doi.org/10.1007/s41478-016-0020-7

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  • DOI: https://doi.org/10.1007/s41478-016-0020-7

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