Discrete Groups On N -dimensional Complex Hyperbolic Space, Stable Basin Theorm And The Fundmental Domain

In recent years, discrete groups on Complex Hyperbolic Space and the fundamental domain are something that mathematicians at home and abroad have paid close attention on. As we know, many papers have been studied for PU(2,1;C),and we have obtained some important results. However, many results of two-dimensional Complex Hyperbolic Space do not still hold in high dimension which is more complex than two-dimensional case.This paper mainly studies n-dimensional Complex Hyperbolic groups PU (n, 1; C), In the study of discrete group, stable basin theorem and discrete criterion in PU (2, 1; C) are important problems. Basmajian and R.Miner [1], Kamiya and John R.Parker [8] have a lot of important achievements.This paper divides into three parts, the first part is that the stable basin theorem in complex two-dimensional situation proved by John. R.Parker [8]can be extended to the stable basin theorem in complex high dimension space, the second part, under certain conditions, on kamiya and John R.Parker [54] discrete criterion of the subgroup of PU (2, 1; C) which contains screw parabolic transform of discrete criterion of will be generalized to high dimension space.