Conformal dimension and Gromov hyperbolic groups with 2-sphere boundary

被引：54

作者：

Bonk, M ^{[1
]}

Kleiner, B ^{[1
]}

机构：

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

来源：

GEOMETRY & TOPOLOGY | 2005年 / 9卷

关键词：

Gromov hyperbolic groups; Cannon's conjecture; quasisymmetric maps;

D O I：

10.2140/gt.2005.9.219

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Suppose G is a Gromov hyperbolic group, and partial derivative(infinity)G is quasisymmetrically homeomorphic to an Ahlfors Q-regular metric 2-sphere Z with Ahlfors regular conformal dimension Q. Then G acts discretely, cocompactly, and isometrically on H-3.

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收藏

页码：219 / 246

页数：28

相关论文

共 23 条

[1] Conformal dimension of the antenna set [J].

Bishop, CJ ;

Tyson, JT .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 129 (12) :3631-3636

[2]

Bonk M, 2002, J DIFFER GEOM, V61, P81

[3] Quasisymmetric parametrizations of two-dimensional metric spheres [J].

Bonk, M ;

Kleiner, B .

INVENTIONES MATHEMATICAE, 2002, 150 (01) :127-183

[4] Conformal metrics on the unit ball in euclidean space [J].

Bonk, M ;

Koskela, P ;

Rohde, S .

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1998, 77 :635-664

[5]

Bourdon M, 2003, J REINE ANGEW MATH, V558, P85

[6] Rigidity of quasi-isometries for some hyperbolic buildings [J].

Bourdon, M ;

Pajot, H .

COMMENTARII MATHEMATICI HELVETICI, 2000, 75 (04) :701-736

[7]

BUYALO S, VOLUME ENTROPY HYPER

[8] Differentiability of Lipschitz functions on metric measure spaces [J].

Cheeger, J .

GEOMETRIC AND FUNCTIONAL ANALYSIS, 1999, 9 (03) :428-517

[9] PATTERSON-SULLIVAN MEASUREMENTS ON THE BOUNDARY OF A GROMOV HYPERBOLIC SPACE [J].

COORNAERT, M .

PACIFIC JOURNAL OF MATHEMATICS, 1993, 159 (02) :241-270

[10]

HAJLASZ P, 2000, MEM AM MATH SOC, V668