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

In [Y.-P. Jiang, S. Kamiya, J.R. Parker, Jøgensen’s inequality for complex hyperbolic space, Geometriae Dedicate 97 (2003) 55–80], Jiang et al. provided Jørgensen’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 Jørgensen’s inequality for the subgroup generated by two elements, but one of which is regular elliptic.