Dirichlet-Ford domains and Double Dirichlet domains

作者：Jespers E^*; Juriaans S O; Kiefer A; e Silva A de A; Souza Filho A C

来源：Bulletin of the Belgian Mathematical Society Simon Stevin, 2016, 23(3): 465-479.

DOI：10.36045/bbms/1473186517

• Hyperbolic space
• Kleinian groups
• Fundamental domains

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 is an element of H-2 or center j is an element of 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.

• 出版日期2016-9