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Sibirsk. Mat. Zh., 2015, Volume 56, Number 5, Pages 1068–1091 (Mi smj2698)  

This article is cited in 8 scientific papers (total in 8 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

Full text: PDF file (426 kB)
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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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\by M.~B.~Karmanova
\paper The area formula for graphs on $4$-dimensional $2$-step sub-Lorentzian structures
\jour Sibirsk. Mat. Zh.
\yr 2015
\vol 56
\issue 5
\pages 1068--1091
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\transl
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\vol 56
\issue 5
\pages 852--871
\crossref{https://doi.org/10.1134/S0037446615050080}
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    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:
    1. M. B. Karmanova, “Maximal graph surfaces on four-dimensional two-step sub-Lorentzian structures”, Siberian Math. J., 57:2 (2016), 274–284  mathnet  crossref  crossref  mathscinet  isi  elib
    2. M. B. Karmanova, “Variations of nonholonomic-valued mappings and their applications to maximal surface theory”, Dokl. Math., 93:3 (2016), 276–279  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    3. M. B. Karmanova, “Area formula for graph surfaces on five-dimensional sub-Lorentzian structures”, Dokl. Math., 93:2 (2016), 216–219  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    4. M. B. Karmanova, “Surface area on two-step sub-Lorentzian structures with multi-dimensional time”, Dokl. Math., 95:3 (2017), 218–221  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    5. M. B. Karmanova, “Graph surfaces on five-dimensional sub-Lorentzian structures”, Siberian Math. J., 58:1 (2017), 91–108  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. M. B. Karmanova, “Maximal surfaces on five-dimensional group structures”, Siberian Math. J., 59:3 (2018), 442–457  mathnet  crossref  crossref  isi  elib
    7. M. B. Karmanova, “Polynomial sub-Riemannian differentiability on Carnot–Carathéodory spaces”, Siberian Math. J., 59:5 (2018), 860–869  mathnet  crossref  crossref  isi  elib
    8. M. B. Karmanova, “Dvustupenchatye sublorentsevy struktury i poverkhnosti-grafiki”, Izv. RAN. Ser. matem., 84:1 (2020), 60–104  mathnet  crossref
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