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
收藏
页码：289 / 312
页数：24
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