A quantitative version of the Morse lemma and quasi-isometries fixing the ideal boundary

被引：7

作者：

Shchur, Vladimir ^{[1
,2
]}

机构：

[1] Univ Paris 11, F-91405 Orsay, France

[2] Ecole Normale Super, F-75230 Paris 05, France

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2013年 / 264卷 / 03期

关键词：

Morse lemma; Quasi-isometry; Quasi-geodesic; Hyperbolic space; Hyperbolic group;

D O I：

10.1016/j.jfa.2012.11.014

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Morse lemma is fundamental in hyperbolic group theory. Using exponential contraction, we establish an upper bound for the Morse lemma that is optimal up to multiplicative constants, which we demonstrate by presenting a concrete example. We also prove an "anti" version of the Morse lemma. We introduce the notion of a geodesically rich space and consider applications of these results to the displacement of points under quasi-isometries that fix the ideal boundary. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：815 / 836

页数：22