ON MAPPINGS OF FINITE DISTORTION THAT ARE QUASICONFORMAL IN THE UNIT DISK

被引：0

作者：

Hirviniemi, Olli ^{[1
]}

Hitruhin, Lauri ^{[1
]}

Prause, Istvan ^{[2
]}

Saksman, Eero ^{[1
]}

机构：

[1] Univ Helsinki, Dept Math & Stat, POB 68, FIN-00014 Helsinki, Finland

[2] Univ Eastern Finland, Dept Phys & Math, POB 111, Joensuu 80101, Finland

来源：

JOURNAL D ANALYSE MATHEMATIQUE | 2023年 / 149卷 / 01期

基金：

欧洲研究理事会;

关键词：

GENERALIZED QUASIDISKS; MODULUS; CONTINUITY;

D O I：

10.1007/s11854-022-0248-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study quasiconformal mappings of the unit disk that have homeomorphic planar extension with controlled distortion. For these mappings we prove a bound for the modulus of continuity of the inverse map, which somewhat surprisingly is almost as good as for global quasiconformal maps. Furthermore, we give examples which improve the known bounds for the three point property of generalized quasidisks. Finally, we establish optimal regularity of such maps when the image of the unit disk has cusp type singularities.

引用

页码：369 / 400

页数：32

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