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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2020, Volume 492, Pages 38–42
DOI: https://doi.org/10.31857/S2686954320030108 (Mi danma69) 		 
This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

Space-likeness of classes of level surfaces on Carnot groups and their metric properties

M. B. Karmanova

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russian Federation
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DOI: https://doi.org/10.31857/S2686954320030108
Abstract: We consider $C^1$-smooth vector functions defined on Carnot groups of arbitrary depth, deduce conditions for space-likeness of their level surfaces, and describe their metric properties from the viewpoint of sub-Lorentzian geometry. We prove the coarea formula as an expression of the measure of a subset of a Carnot group in terms of the sub-Lorentzian measures of its intersections with level sets of a vector function.
Keywords: Carnot group, sub-Lorentzian structure, vector function, level set, sub-Lorentzian measure, coarea formula.
Funding agency Grant number
Mathematical Center in Akademgorodok 075-15-2019-1613
This work was supported by Mathematical Center in Akademgorodok under agreement no. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation.
Presented: Yu. G. Reshetnyak
Received: 20.02.2020
Revised: 20.02.2020
Accepted: 10.04.2020
English version:
Doklady Mathematics, 2020, Volume 101, Issue 3, Pages 205–208
DOI: https://doi.org/10.1134/S1064562420030102
Bibliographic databases:
Document Type: Article
UDC: 517.518.182+517.518.114+514.7
Language: Russian
Citation: M. B. Karmanova, “Space-likeness of classes of level surfaces on Carnot groups and their metric properties”, Dokl. RAN. Math. Inf. Proc. Upr., 492 (2020), 38–42; Dokl. Math., 101:3 (2020), 205–208
Citation in format AMSBIB
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\by M.~B.~Karmanova
\paper Space-likeness of classes of level surfaces on Carnot groups and their metric properties
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2020
\vol 492
\pages 38--42
\mathnet{http://mi.mathnet.ru/danma69}
\crossref{https://doi.org/10.31857/S2686954320030108}
\zmath{https://zbmath.org/?q=an:1480.53047}
\elib{https://elibrary.ru/item.asp?id=42929995}
\transl
\jour Dokl. Math.
\yr 2020
\vol 101
\issue 3
\pages 205--208
\crossref{https://doi.org/10.1134/S1064562420030102}
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    • This publication is cited in the following 1 articles:
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    		Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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