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

页码：525 / 539

页数：15

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