Busemann函数和素端

发布时间：2018-04-26 13:13

本文选题：素端 + Busemann函数　；参考：《四川师范大学》2015年硕士论文

【摘要】：研究复杂区域的边界对应问题往往是十分困难的Caratheodoy最早提出素端的概念,为人们在解决这类问题时提供了良好的工具.随后,人们也对素端给出了不同的刻画,并将该思想应用到其它研究领域.如在复动力系统中研究Julia集的性质Busemann是定义在无界完备的度量空间上的连续函数,可以利用Busemann函数讨论无穷边界的性质.而在复平面上任一边界多于两点的单连通区域上可赋有Poincare度量,它在该区域上是无界完备的度量,相应地可在这个度量下定义Busemann函数.本文主要应用Busemann函数的相关理论和方法来讨论素端.在第二章介绍了素端的概念,并且介绍了Poincare度量的相关性质以及Buesmann函数的概念和它的一些性质.第三章介绍了单位圆上的Busemann函数和极限球与边界点的对应关系,进而研究了它们与素端的联系.
[Abstract]:It is difficult for Caratheodoy to study the boundary correspondence problem of complex regions. It is the first time that Caratheodoy put forward the concept of prime end, which provides a good tool for people to solve this kind of problems. Subsequently, different characterizations of prime end are given, and the idea is applied to other research fields. If we study the properties of Julia sets in complex dynamical systems, Busemann is a continuous function defined on an unbounded complete metric space, we can use Busemann functions to discuss the properties of infinite boundaries. The Poincare metric can be obtained on a simple connected domain with more than two boundaries in the complex plane. It is an unbounded and complete metric in this region. Accordingly, the Busemann function can be defined in this metric. In this paper, we use the theory and method of Busemann function to discuss the prime end. In the second chapter, we introduce the concept of prime end, and introduce the related properties of Poincare metric, the concept of Buesmann function and some properties of it. In chapter 3, we introduce the Busemann function and the relation between the limit sphere and the boundary point on the unit circle, and then study the relation between them and the prime end.
【学位授予单位】：四川师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O174

【共引文献】