caa a22 4500 469117281 CHVBK 20180323133128.0 cr unu---uuuuu 170328e19921201xx s 000 0 eng 10.1007/BF02921576 doi (NATIONALLICENCE)springer-10.1007/BF02921576 Dirichlet polyhedra for dihedral groups acting on complex hyperbolic space [Elektronische Daten] [William Goldman, John Parker] We consider groups Γ generated by inversions in a pair of asymptotic complex hyperplanes in complex hyperbolic spaceH ℂ n . We show that there exists a Γ-invariant real hypersurfaceF ⊂H ℂ n such that the Dirichlet fundamental polyhedron for Γ centered at z0 has two sides (resp. infinitely many sides) if and only ifz 0 ∈F (resp.z 0 ∉F). The Dirichlet regions are determined explicitly in terms of coordinates on Γ-invariant horospheres and the geometry ofH ℂ n is developed in terms of these horospherical coordinates. CRC Press, Inc, 1992 Goldman William University of Maryland, Department of Mathematics, 20742, College, Park, MD, USA aut Parker John Mathematics Institute, University of Warwick, CV4 7AL, Coventry, UK aut The Journal of Geometric Analysis Springer-Verlag 2/6(1992-12-01), 517-554 1050-6926 2:6<517 1992 2 12220 https://doi.org/10.1007/BF02921576 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02921576 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Goldman William University of Maryland, Department of Mathematics, 20742, College, Park, MD, USA aut NATIONALLICENCE 700 1- Parker John Mathematics Institute, University of Warwick, CV4 7AL, Coventry, UK aut NATIONALLICENCE 773 0- The Journal of Geometric Analysis Springer-Verlag 2/6(1992-12-01), 517-554 1050-6926 2:6<517 1992 2 12220 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer