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

共 29 条

[1] [Anonymous], 1990, FRACTAL GEOMETRY
[2] AREA DISTORTION OF QUASI-CONFORMAL MAPPINGS
ASTALA, K
[J]. ACTA MATHEMATICA, 1994, 173 (01) : 37 - 60
[3] Balogh ZM, 2000, DUKE MATH J, V101, P555
[4] Balon R, 1999, J SEX MARITAL THER, V25, P259
[5] Basmajian A, 1998, INVENT MATH, V131, P85
[6] Bellaiche A., 1996, PROGR MATH, V144, P4
[7] Bishop CJ, 1999, ANN ACAD SCI FENN-M, V24, P397
[8] BISHOP CJ, CONFORMAL DIMENSION
[9] BISHOP CJ, IN PRESS ANN ACAD SC
[10] AT THE BOUNDARY OF SOME HYPERBOLIC POLYHEDRA
BOURDON, M
[J]. ANNALES DE L INSTITUT FOURIER, 1995, 45 (01) : 119 - 141

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