Classes of Noncontact Mappings of Carnot Groups and Metric Properties

Classes of Noncontact Mappings of Carnot Groups and Metric Properties Full article

Journal

Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260

Output data

Year: 2023, Volume: 64, Number: 6, Pages: 1330-1350 Pages count : 21 DOI: 10.1134/S0037446623060083

Funding (1)

Министерство науки и высшего образования РФ
Mathematical Center in Akademgorodok

075-15-2019-1613, 075-15-2022-281

We study the metric properties of level surfaces for classes of smooth noncontact mappings from arbitrary Carnot groups into two-step ones with some constraints on the dimensions of horizontal subbundles and the subbundles corresponding to degree 2 fields. We calculate the Hausdorff dimension of the level surfaces with respect to the sub-Riemannian quasimetric and derive an analytical relation between the Hausdorff measures for the sub-Riemannian quasimetric and the Riemannian metric. As application, we establish a new form of coarea formula, also proving that the new coarea factor is well defined.

Karmanova M.B.
Classes of Noncontact Mappings of Carnot Groups and Metric Properties
Siberian Mathematical Journal. 2023. V.64. N6. P.1330-1350. DOI: 10.1134/S0037446623060083 WOS Scopus РИНЦ OpenAlex

Карманова М.Б.
Классы неконтактных отображений групп Карно и метрические свойства
Сибирский математический журнал. 2023. Т.64. №6. С.1199-1223. DOI: 10.33048/smzh.2023.64.608 РИНЦ

Submitted:	Apr 25, 2023
Accepted:	Sep 25, 2023
Published print:	Nov 24, 2023
Published online:	Nov 24, 2023

Web of science:	WOS:001120902100001
Scopus:	2-s2.0-85178939062
Elibrary:	64523909
OpenAlex:	W4389379234

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