Hausdorff dimension distribution of quasiconformal mappings on the heisenberg group

被引：35

作者：

Balogh, ZM ^{[1
]}

机构：

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

来源：

JOURNAL D ANALYSE MATHEMATIQUE | 2001年 / 83卷 / 1期

关键词：

D O I：

10.1007/BF02790265

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct quasiconformal mappings on the Heisenberg group which change the Hausdorff dimension of Cantor-type sets in an arbitrary fashion. On the other hand, we give examples of subsets of the Heisenberg group whose Hausdorff dimension cannot be lowered by any quasiconformal mapping. For a general set of a certain Hausdorff dimension we obtain estimates of the Hausdorff dimension of the image set in terms of the magnitude of the quasiconformal distortion.

引用

页码：289 / 312

页数：24

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