On Local Metric Characteristics of Level Sets of CH1-Mappings of Carnot Manifolds

被引：0
作者：
M. B. Karmanova
机构：
[1] Sobolev Institute of Mathematics,
来源：
Siberian Mathematical Journal | 2019年 / 60卷
关键词：
Carnot—Carathéodory space; Carnot group; Lipschitz mapping; induced measure; adapted basis; area formula;
D O I：
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中图分类号：
学科分类号：
摘要：
Considering the level surfaces of the mappings of class CH1 which are defined on Carnot manifolds and take values in Carnot—Carathéodory spaces, we introduce some adequate local metric characteristic that bases on a correspondence with a neighborhood of the kernel of the sub-Riemannian differential. Moreover, for the mappings on Carnot groups we construct an adapted basis in the preimage which matches local sub-Riemannian structures on the complement of the kernel of the sub-Riemannian differential (including those meeting the level set) and on the arrival set.
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页码：1007 / 1021
页数：14
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