Discreteness of subgroups of PU(2,1) with regular elliptic elements

摘要

In [Y.-P. Jiang, S. Kamiya, J.R. Parker, Jogensen's inequality for complex hyperbolic space, Geometriae Dedicate 97 (2003) 55-80], Jiang et al. provided Jorgensen's inequality for non-elementary group of isometries of complex hyperbolic space generated by two elements, one of which is loxodromic or boundary elliptic. In this paper, we give analogues of Jorgensen's inequality for the subgroup generated by two elements, but one of which is regular elliptic. (C) 2007 Published by Elsevier Inc.