Carnot rectifiability of sub-Riemannian manifolds with constant tangent

被引：0

作者：

Le Donne, Enrico ^{[1
,2
]}

Young, Robert ^{[3
]}

机构：

[1] Univ Fribourg, Dept Math, Chemin Musee 23, CH-1700 Fribourg, Switzerland

[2] Univ Jyvaskyla, Dept Math & Stat, FI-40014 Jyvaskyla, Finland

[3] NYU, Courant Inst Math Sci, 251 Mercer St, New York, NY 10012 USA

来源：

ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE | 2023年 / 24卷 / 01期

基金：

欧洲研究理事会; 芬兰科学院;

关键词：

SPACES;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that if M is a sub-Riemannian manifold and N is a Carnot group such that the nilpotentization of M at almost every point is isomorphic to N, then there are subsets of N of positive measure that embed into M by biLipschitz maps. Furthermore, M is countably N-rectifiable, i.e., all of M except for a null set can be covered by countably many such maps.

引用

页码：71 / 96

页数：26

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