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This article is cited in 9 scientific papers (total in 9 papers)
The area formula for graphs on $4$-dimensional $2$-step sub-Lorentzian structures
M. B. Karmanova
Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
Abstract:
We study graph surfaces on $4$-dimensional $2$-step sub-Lorentzian structures, deduce their differential properties, and prove area formulas for various sub-Lorentzian measures.
Keywords:
sub-Lorentzian geometry, graph surface, area formula, Hausdorff measure.
DOI:
https://doi.org/10.17377/smzh.2015.56.508
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English version:
Siberian Mathematical Journal, 2015, 56:5, 852–871
Bibliographic databases:
  
UDC:
514.747+517.518.15
Received: 25.01.2015
Citation:
M. B. Karmanova, “The area formula for graphs on $4$-dimensional $2$-step sub-Lorentzian structures”, Sibirsk. Mat. Zh., 56:5 (2015), 1068–1091; Siberian Math. J., 56:5 (2015), 852–871
Citation in format AMSBIB
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\issue 5
\pages 852--871
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Linking options:
http://mi.mathnet.ru/eng/smj2698 http://mi.mathnet.ru/eng/smj/v56/i5/p1068
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:
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M. B. Karmanova, “Maximal graph surfaces on four-dimensional two-step sub-Lorentzian structures”, Siberian Math. J., 57:2 (2016), 274–284
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M. B. Karmanova, “Variations of nonholonomic-valued mappings and their applications to maximal surface theory”, Dokl. Math., 93:3 (2016), 276–279
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M. B. Karmanova, “Area formula for graph surfaces on five-dimensional sub-Lorentzian structures”, Dokl. Math., 93:2 (2016), 216–219
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M. B. Karmanova, “Surface area on two-step sub-Lorentzian structures with multi-dimensional time”, Dokl. Math., 95:3 (2017), 218–221
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M. B. Karmanova, “Graph surfaces on five-dimensional sub-Lorentzian structures”, Siberian Math. J., 58:1 (2017), 91–108
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M. B. Karmanova, “Maximal surfaces on five-dimensional group structures”, Siberian Math. J., 59:3 (2018), 442–457
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M. B. Karmanova, “Polynomial sub-Riemannian differentiability on Carnot–Carathéodory spaces”, Siberian Math. J., 59:5 (2018), 860–869
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M. B. Karmanova, “Two-step sub-Lorentzian structures and graph surfaces”, Izv. Math., 84:1 (2020), 52–94
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M. B. Karmanova, “Ploschad grafikov na proizvolnykh gruppakh Karno s sublorentsevoi strukturoi”, Sib. matem. zhurn., 61:4 (2020), 823–848
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