The Limit Points Of A Discrete Subgroup In Complex Hyperbolic Space

The main purpose of this thesis studies the limit sets of discrete subgroups incomplex hyperbolic space, firstly we obtain the necessary and su?cient conditionsthat the complex hyperbolic groups are the elementary groups, these are general-ized conclusions of isometry transformation groups which act on real hyperbolicspace. Then we study several results of the classification of the limit points aboutnonelementary discrete subgroups in complex hyperbolic space, and portray thecharacteristics of the line transitive points, the point transitive points, the points ofapproximation of nonelementary discrete subgroups in complex hyperbolic space.That a fixed point of a loxodromic element must be a point of approximation isproven in this chapter. The relations between the Dirichlet points and the pointsof approximation are discussed. Also which the points of approximation are notthe Dirichlet points are proven in this artical.