Stability of isometric maps in the Heisenberg group

被引：0

作者：

Arcozzi, Nicola ^{[1
]}

Morbidelli, Daniele ^{[1
]}

机构：

[1] Univ Bologna, Dipartmento Matemat, I-40127 Bologna, Italy

来源：

COMMENTARII MATHEMATICI HELVETICI | 2008年 / 83卷 / 01期

关键词：

Heisenberg group; subRiemannian geometry; biLipschitz maps;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we prove approximation results for biLipschitz maps in the Heisenberg group. Namely, we show that a biLipschitz map with biLipschitz constant close to one can be pointwise approximated, quantitatively in any fixed ball, by an isometry. This leads to an approximation in BMO norm for the map's Pansu derivative. We also prove that a global quasigeodesic can be approximated by a geodesic on any fixed segment.

引用

页码：101 / 141

页数：41

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