Local approximation of uniformly regular Carnot-Caratheodory quasispaces by their tangent cones

被引：14

作者：

Greshnov, A. V. ^{[1
]}

机构：

[1] Sobolev Inst Math, Novosibirsk, Russia

来源：

SIBERIAN MATHEMATICAL JOURNAL | 2007年 / 48卷 / 02期

基金：

俄罗斯基础研究基金会;

关键词：

Carnot-Caratheodory space; quasimetric; nilpotent group; local approximation theorem; Gromov-Hausdorff convergence;

D O I：

10.1007/s11202-007-0024-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a local approximation theorem for the Carnot-Caratheodory quasimetrics on uniformly regular (equiregular) Carnot-Caratheodory spaces. Using this theorem, we study convergence of the Carnot-Caratheodory quasispaces to their tangent cones. In particular, we prove a Mitchell type theorem on convergence of an equiregular Carnot-Caratheodory quasispace with distinguished point to its tangent cone.

引用

页码：229 / 248

页数：20

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