Interplay between interior and boundary geometry in Gromov hyperbolic spaces

被引：11
|
作者：
Jordi, Julian [1 ]
机构：
[1] Univ Zurich, Inst Math, CH-8057 Zurich, Switzerland
来源：
GEOMETRIAE DEDICATA | 2010年 / 149卷 / 01期
基金：
瑞士国家科学基金会;
关键词：
Hyperbolic spaces; Boundary at infinity; Quasimetric; Quasisymmetric maps; Quasimoebius maps;
D O I：
10.1007/s10711-010-9472-0
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that two visual and geodesic Gromov hyperbolic metric spaces are roughly isometric if and only if their boundaries at infinity, equipped with suitable quasimetrics, are bilipschitz-quasimoebius equivalent. Similarly, they are quasi-isometric if and only if their boundaries are power quasimoebius equivalent.
引用
收藏
页码：129 / 154
页数：26
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