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september 2016 Dirichlet-Ford domains and Double Dirichlet domains
E. Jespers, S. O. Juriaans, A. Kiefer, A. de A. e Silva, A. C. Souza Filho
Bull. Belg. Math. Soc. Simon Stevin 23(3): 465-479 (september 2016). DOI: 10.36045/bbms/1473186517

Abstract

We continue investigations started by Lakeland on Fuchsian and Kleinian groups which have a Dirichlet fundamental domain that also is a Ford domain in the upper half-space model of hyperbolic $2$- and $3$-space, or which have a Dirichlet domain with multiple centers. Such domains are called DF-domains and Double Dirichlet domains respectively. Making use of earlier obtained concrete formulas for the bisectors defining the Dirichlet domain of center $i \in \mathbb H^2$ or center $j \in \mathbb H^3$, we obtain a simple condition on the matrix entries of the side-pairing transformations of the fundamental domain of a Fuchsian or Kleinian group to be a DF-domain. Using the same methods, we also complement a result of Lakeland stating that a cofinite Fuchsian group has a DF domain (or a Dirichlet domain with multiple centers) if and only if it is an index $2$ subgroup of the discrete group G of reflections in a hyperbolic polygon.

Citation

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E. Jespers. S. O. Juriaans. A. Kiefer. A. de A. e Silva. A. C. Souza Filho. "Dirichlet-Ford domains and Double Dirichlet domains." Bull. Belg. Math. Soc. Simon Stevin 23 (3) 465 - 479, september 2016. https://doi.org/10.36045/bbms/1473186517

Information

Published: september 2016
First available in Project Euclid: 6 September 2016

zbMATH: 06643015
MathSciNet: MR3545464
Digital Object Identifier: 10.36045/bbms/1473186517

Subjects:
Primary: 20H10 , 30F40
Secondary: 51M10 , 57M60

Keywords: Fundamental domains , Hyperbolic space , Kleinian groups

Rights: Copyright © 2016 The Belgian Mathematical Society

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Vol.23 • No. 3 • september 2016
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