Level Sets of Classes of Mappings of Two-Step Carnot Groups in a Nonholonomic Interpretation

Сибирский математический журнал

M. B. Karmanova¹ 

[1] Sobolev Institute of Mathematics

关键词: two-step Carnot group;    level set;    Hausdorff dimension;    coarea formula;   

DOI  :  10.1134/S0037446619020101

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

We obtain the metric properties of level sets of certain sufficiently smooth mappings of two-step Carnot groups which are Hölder in the sub-Riemannian sense. In particular, we calculate the Hausdorff dimension of these sets and prove a coarea formula of a new type.

【 授权许可】

CC BY