Absolute continuity of quasiconformal mappings on curves

被引：36

作者：

Balogh, Zoltan M.

Koskela, Pekka

Rogovin, Sari

机构：

[1] Univ Bern, Inst Math, CH-3012 Bern, Switzerland

[2] Univ Jyvaskyla, Dept Math & Stat, FIN-40014 Jyvaskyla, Finland

来源：

GEOMETRIC AND FUNCTIONAL ANALYSIS | 2007年 / 17卷 / 03期

基金：

芬兰科学院;

关键词：

absolute continuity; quasiconformal mappings; metricmeasure spaces;

D O I：

10.1007/s00039-007-0607-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that a quasiconformal mapping between two proper, locally Ahlfors Q-regular metric spaces, Q > 1, is absolutely continuous on almost every curve. We further relax the limes superior in the definition of quasiconformality to a limes inferior and verify that exceptional sets analogous to the Euclidean setting can be allowed.

引用

页码：645 / 664

页数：20

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