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.
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).
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
\Bibitem{Kar21}
\by M.~B.~Karmanova
\paper The coarea formula for vector functions on Carnot groups with sub-Lorentzian structure
\jour Sibirsk. Mat. Zh.
\yr 2021
\vol 62
\issue 2
\pages 298--325
\mathnet{http://mi.mathnet.ru/smj7557}
\crossref{https://doi.org/10.33048/smzh.2021.62.205}
\elib{https://elibrary.ru/item.asp?id=44949139}
\transl
\jour Siberian Math. J.
\yr 2021
\vol 62
\issue 2
\pages 239--261
\crossref{https://doi.org/10.1134/S0037446621020051}
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Linking options:
https://www.mathnet.ru/eng/smj7557
https://www.mathnet.ru/eng/smj/v62/i2/p298
This publication is cited in the following 8 articles:
M. B. Karmanova, “The Area of Images of Classes of Measurable Sets on Carnot Groups with Sub-Lorentzian Structure”, Sib Math J, 65:5 (2024), 1116
M. B. Karmanova, “Ploschad obrazov klassov izmerimykh mnozhestv na gruppakh Karno s sublorentsevoi strukturoi”, Sib. matem. zhurn., 65:5 (2024), 926–952
M. B. Karmanova, “Klassy nekontaktnykh otobrazhenii grupp Karno i metricheskie svoistva”, Sib. matem. zhurn., 64:6 (2023), 1199–1223
M. B. Karmanova, “Classes of Noncontact Mappings of Carnot Groups and Metric Properties”, Sib Math J, 64:6 (2023), 1330
M. B. Karmanova, “Lipschitz images of open sets on sub-Lorentzian structures”, Siberian Adv. Math., 34:1 (2024), 67–79
M. B. Karmanova, “The area of surfaces on sub-Lorentzian structures of depth two”, Siberian Adv. Math., 33:3 (2023), 214–229
M. B. Karmanova, “Sub-Lorentzian coarea formula for mappings of Carnot groups”, Siberian Math. J., 63:3 (2022), 485–508
M. B. Karmanova, “Sub-riemannian properties of the level sets of noncontact mappings of Heisenberg groups”, Siberian Adv. Math., 33:1 (2023), 28–38
Citation in format AMSBIB
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