高维Klein群的组合定理及其应用

项目名称： 高维Klein群的组合定理及其应用

项目编号： No.11201130

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 李浏兰

作者单位： 衡阳师范学院

项目金额： 22万元

中文摘要： 组合定理是Klein群理论的一个经典研究问题,围绕该问题已经有一系列的研究成果。我们已经把第一个Klein-Maskit组合定理推广到高维实Klein群上，本项目将继续开展该研究，拟将第二个Klein-Maskit组合定理推广到高维实Klein群上，并应用于高维实Klein群的构造和高维实双曲流形的分解与合成；同时探讨组合定理在高维复Klein群上的推广及应用，以此推进高维复双曲流形的研究。具体的研究内容是：（1）第二个Klein-Maskit组合定理在高维实Klein群上的推广；（2）高维实Klein群的构造；（3）高维Klein-Maskit组合定理在高维实双曲流形上的应用；（4）组合定理在高维复Klein群上的推广及应用。

中文关键词： 组合定理；Klein群；高维；流形；调和映射

英文摘要： In the theory of Kleinian groups, there is a classical research problem called combination theorems, on which there are a series of results. We have generalized the first Klein-Maskit combination theorem to high-dimensional real Kleinian groups. In this project, we will continue to carry out this research, plan to generalize the second Klein-Maskit combination theorem to high-dimensional real Kleinian groups and apply our results in the constructions of high-dimensioanl real Kleinian groups and the decompositions and compositions of high-dimensional real hyperbolic manifolds. Meanwhile, we will explore the generalizations and applications of combination theorems on high-dimensional complex Kleinian groups in order to promote the research of the high-dimensional complex hyperbolic manifolds. The detailed research contents are as follows: 1) the generalization of the second Klein-Maskit combination theorem to high-dimensional real Kleinian groups；2) the constructions of high-dimensional real Kleinian groups；3) the applications of Klein-Maskit combination theorems in high-dimensional real hyperbolic manifolds；4) the generalizations and applications of combination theorems in high-dimensional complex Klienian groups.

英文关键词： combination theorems；Kleinian group；higher dimension；manifold；harmonic mappings