Reference : Dirichlet-Ford domains and double Dirichlet domains
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Dirichlet-Ford domains and double Dirichlet domains
Jespers, E. mailto [> >]
Juriaans, S. O. mailto [> >]
Kiefer, Ann mailto [University of Luxembourg > Faculty of Humanities, Education and Social Sciences (FHSE) > LUCET]
de A. e Silva, A. mailto [> >]
Souza Filho, A. C. mailto [> >]
Bulletin of the Belgian Mathematical Society Simon Stevin
Yes (verified by ORBilu)
[en] Hyperbolic Space ; Kleinian Groups ; Fundamental Domains
[en] 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 ∈ H 2 or center j ∈ 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.

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