Circle packing with generalized branching

Edward T Crane; Kenneth Stephenson; James Ashe

doi:10.1007/s41478-016-0020-7

Circle packing with generalized branching

Edward T Crane, Kenneth Stephenson, James Ashe

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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Abstract

Attempts to build a discrete theory for rational maps on the sphere via circle packing have foundered on discretization effects in locating branch points. The authors remove this impediment by introducing generalized branch points. A generalized branch point need no longer be attached to an individual circle, but with the help of chaperones and other devices, can be positioned anywhere that the geometry requires. The effects are illustrated in images and videos as we use generalized branching to fix flaws in discrete Ahlfors and Weierstrass functions.

Original language	English
Pages (from-to)	251–276
Number of pages	28
Journal	Journal of Analysis
Volume	24
Issue number	2
Early online date	8 Dec 2016
DOIs	https://doi.org/10.1007/s41478-016-0020-7
Publication status	Published - Dec 2016

Keywords

Circle packing
Discrete analytic function
Blaschke product
Ahlfors function
Branch point

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10.1007/s41478-016-0020-7

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This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Springer at http://link.springer.com/article/10.1007/s41478-016-0020-7. Please refer to any applicable terms of use of the publisher.
Accepted author manuscript, 6.43 MBLicence: CC BY-NC

http://arxiv.org/abs/1607.03404

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Dr Edward T Crane
- Edward.Crane@bristol.ac.uk
- School of Mathematics - Heilbronn Senior Research Fellow
- Probability, Analysis and Dynamics
- Heilbronn Institute for Mathematical Research
- Pure Mathematics
Person: Academic , Member

Cite this

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KW - Ahlfors function

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Circle packing with generalized branching

Abstract

Keywords

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Dr Edward T Crane

Cite this