Abstract:
We prove a sub-Lorentzian analog of the area formula for intrinsically Lipschitz mappings of open subsets of Carnot groups of arbitrary depth with a sub-Lorentzian structure introduced on the image space.
Key words:
sub-Riemannian quasimetric, open set, Lipschitz mapping, Carnot group, sub-Lorentzian structure, Hausdorff measure, area formula.
Citation:
M. B. Karmanova, “Lipschitz images of open sets on sub-Lorentzian structures”, Mat. Tr., 26:2 (2023), 138–161; Siberian Adv. Math., 34:1 (2024), 67–79
\Bibitem{Kar23}
\by M.~B.~Karmanova
\paper Lipschitz images of open sets on sub-Lorentzian structures
\jour Mat. Tr.
\yr 2023
\vol 26
\issue 2
\pages 138--161
\mathnet{http://mi.mathnet.ru/mt683}
\crossref{https://doi.org/10.33048/mattrudy.2023.26.207}
\transl
\jour Siberian Adv. Math.
\yr 2024
\vol 34
\issue 1
\pages 67--79
\crossref{https://doi.org/10.1134/S1055134424010036}
Linking options:
https://www.mathnet.ru/eng/mt683
https://www.mathnet.ru/eng/mt/v26/i2/p138
This publication is cited in the following 4 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, “Metric characteristics of classes of compact sets on Carnot groups with sub-Lorentzian structure”, Vladikavk. matem. zhurn., 26:3 (2024), 56–64
M. B. Karmanova, “Area of images of measurable sets on depth 2 Carnot manifolds with sub-Lorentzian structure”, Vladikavk. matem. zhurn., 26:4 (2024), 78–86
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