Deformation theory of Kleinian groups

1.利用双曲流形的几何性质，给出了n维双曲离散群的极限的Hausdorff维数小于n.2的必要条件.我们研究了当Kleinian群变形时Hausdorff维数的连续性.分析了参数空间中离散表示集的结构，提出了从黎曼流形上的投影空间出发，利用完整映射分析拟Fuchsian群空间结构的方法.得到了Kleinian群在小扰动下的结构稳定性以及拟共形变形空间中代数拓扑与Teichm_ller拓扑的等价性.我们在Teichm_ller空间的基础上建立了整函数动力系统的变形理论，发现了有理函数所不具备的游动域和Baker域的基本性质。6.本文研究了一类镶嵌函数族，证明了它的拓扑完备性，并给出了这类函数的Fatou分支的Teichm_ller空间。

1. By geometric properties of corresponding a hyperbolic manifold we described the necessary conditions in order that the Hausdorff dimension of the limite of a n-dimensinal hyperbolic discrete group is less than n.2. We investigated the continuity of the Hausdorff dimensions as the Kleinian groups are deformed.3. We analized the structures of the set of discrete representations in the parameter space and proposed the method of analizing the structure of the space of quasi-Fuchsian groups by a holonomy map from the space of projections on a Riemann manifold.4. We obtained the results on the structural stability of Kleinian groups under small perturbations and on the equivalence between the algebraic topology and the Teichm_ller one in the space of quasiconformal deformations.5. We built the deformation theory of dynamical systems for entire functions on a ground of Teichm_ller space and found the fundamental properties of wan-dering domains and Baker domains, which rational functions don't have.6. We investigated a family of inlaid functions and showed the topological completeness of it. Further we found the Teichm_ller spaces of the Fatou components of those functions.