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

1)对于边界为椭圆或直线元离散的PU（1,2；C）子群，我们得到了Jorgensen不等式的复数形式。我们推广了Kamiya， Basmajian-Miner的稳定盆地定理，用来推广Basmajian-Miner的结果。对于具有螺旋抛物型元的PU（1,2；C）子群，我们也得到了Shinizu引理的复形，用于构造精确不变区域。2)定义了PU（1,n；C）元素的广义等距。利用PU（1,n；C）的离散子群的元的广义等距球，构造了一个基本定域，作为Ford定域的推广。我们展示了广义福特定义域和狄利克雷多面体之间的联系。3)现在我们准备研究变形空间。

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.