STUDY ON CONDITIONS FOR A SUBGROUP OF PU(1,n ; C) ACTING ON COMPLEX HYPERBOLIC SPACE TO BE DISCRETE

1)对于边界椭圆或斜行元素离散的PU(1，2；C)的子群，我们得到了Jorgensen不等式的复数形式。推广了Kamiya、BasMajian-Miner的稳定盆定理，推广了BasMajian-Miner的结果。我们还得到了PU(1，2；C)的一个子群的复数形式的Shinizu引理，用于构造一个精确不变区域。利用PU(1，n；C)的离散子群的元素的广义等距球面，我们构造了一个基本域，它是Ford域的推广。3)现在我们准备研究形变空间。

1)We have complex version of Jorgensen's inequality for a subgroups of PU(1,2;C) with boundary elliptic or loxodromic elements to be discrete. We extend stable basin theorems of Kamiya, Basmajian-Miner, which use to generalize Basmajian-Miner's results. We also obtain complex version of Shinizu's lemma for a subgrou of PU(1,2;C) with screw parabolic elements, which is used to construct a precisely invariant region.2)We define the generalized isometric of an element of PU(1,n;C). By using the generalized isometric spheres of elements of a discrete subgroup of PU(1,n;C), we construct a fundamental domain, which is regarded as a generalization of the Ford domain. And we show the connection between this generalized Ford domain and Dirichlet polyhedron.3)Now we are ready to study the deformation space.