Dirichlet polyhedra for dihedral groups acting on complex hyperbolic space
- Cite this article as:
- Goldman, W.M. & Parker, J.R. J Geom Anal (1992) 2: 517. doi:10.1007/BF02921576
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We consider groups Γ generated by inversions in a pair of asymptotic complex hyperplanes in complex hyperbolic spaceHℂn. We show that there exists a Γ-invariant real hypersurfaceF ⊂Hℂn such that the Dirichlet fundamental polyhedron for Γ centered at z0 has two sides (resp. infinitely many sides) if and only ifz0 ∈F (resp.z0 ∉F). The Dirichlet regions are determined explicitly in terms of coordinates on Γ-invariant horospheres and the geometry ofHℂn is developed in terms of these horospherical coordinates.