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Sibirskii Matematicheskii Zhurnal, 2021, Volume 62, Number 2, Pages 298–325
DOI: https://doi.org/10.33048/smzh.2021.62.205 (Mi smj7557) 		 
This article is cited in 8 scientific papers (total in 8 papers)

The coarea formula for vector functions on Carnot groups with sub-Lorentzian structure

M. B. Karmanova

Sobolev Institute of Mathematics, Novosibirsk, Russia
Full-text PDF (608 kB) Citations (8)
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DOI: https://doi.org/10.33048/smzh.2021.62.205
Abstract: We establish the coarea formula as an expression for the measure of a subset of a Carnot group in terms of the sub-Lorentzian measure of the intersections of the subset with the level sets of a vector function. We describe the conditions for the level sets of vector functions to be spacelike and find the metric characteristics of these surfaces. Also, we address a series of relevant questions, in particular, about the uniqueness of the coarea factor.
Keywords: Carnot group, sub-Lorentzian structure, vector function, level set, sub-Lorentzian measure, coarea formula.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2019-1613
The author was supported by the Mathematical Center in Akademgorodok (Agreement No. 075–15–2019–1613 with the Ministry of Science and Higher Education of the Russian Federation).
Received: 08.06.2020
Revised: 03.10.2020
Accepted: 09.10.2020
English version:
Siberian Mathematical Journal, 2021, Volume 62, Issue 2, Pages 239–261
DOI: https://doi.org/10.1134/S0037446621020051
Bibliographic databases:
Document Type: Article
UDC: 517.518.182+517.518.114+514.7
MSC: 35R30
Language: Russian
Citation: M. B. Karmanova, “The coarea formula for vector functions on Carnot groups with sub-Lorentzian structure”, Sibirsk. Mat. Zh., 62:2 (2021), 298–325; Siberian Math. J., 62:2 (2021), 239–261
Citation in format AMSBIB
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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