Uniformization of SierpiAski carpets in the plane
成果类型：
Article
署名作者：
Bonk, Mario
署名单位：
University of California System; University of California Los Angeles
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910
DOI：
10.1007/s00222-011-0325-8
发表日期：
2011
页码：
559-665
关键词：
摘要：
Let S-i, i is an element of I, be a countable collection of Jordan curves in the extended complex plane (C) over cap that bound pairwise disjoint closed Jordan regions. If the Jordan curves are uniform quasicircles and are uniformly relatively separated, then there exists a quasiconformal map f : (C) over cap -> (C) over cap such that f (S-i) is a round circle for all i is an element of I. This implies that every Sierpinski carpet in (C) over cap whose peripheral circles are uniformly relatively separated uniform quasicircles can be mapped to a round Sierpinski carpet by a quasisymmetric map.