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

页码：129 / 154

页数：26

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