Swiss Cheese, Dendrites, and Quasiconformal Homogeneity

被引：0
|
作者：
Nakki, Raimo [1 ]
Palka, Bruce [2 ]
机构：
[1] Univ Jyvaskyla, Dept Math, SF-40351 Jyvaskyla, Finland
[2] Natl Sci Fdn, Div Math Sci, Arlington, VA 22230 USA
来源：
COMPUTATIONAL METHODS AND FUNCTION THEORY | 2014年 / 14卷 / 2-3期
基金：
美国国家科学基金会;
关键词：
Quasiconformal mapping; Quasiconformally homogeneous domain; Swiss cheese; Dendrite; KLEINIAN-GROUPS; DOMAINS; PLANE;
D O I：
10.1007/s40315-014-0059-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Suppose that is a simply connected domain in the extended complex plane with the following homogeneity property: for each pair of points and in there exists a -quasiconformal self-mapping of such that and . This paper classifies the simply connected plane domains with locally connected boundaries that exhibit this property for some . Any such domain falls into one of five (non-empty) categories, each specified by the character of the boundary of , namely is the empty set, a singleton, a quasicircle, a dendrite, or a Swiss cheese.
引用
收藏
页码：525 / 539
页数：15
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