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Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2013, Volume 13, Issue 4, Pages 16–36 (Mi vngu311)  

This article is cited in 2 scientific papers (total in 2 papers)

One-Dimensional Level Sets of $hc$-Differentiable Mappings of Carnot–Carathéodory Spaces

S. G. Basalaev

Novosibirsk State University

Abstract: We study continuously $hc$-differentiable mappings from the Carnot–Carathéodory space $\mathcal{M}$ such that $\dim H_g \mathcal{M} = \dim T_g \mathcal{M} -1 = N$ in every $g \in \mathcal{M}$ into the Euclidean $N$-dimensional space with the property that $hc$-differential of the mapping is surjective. We establish that the level set of such mapping is a curve that has Hausdorff dimension 2 in sub-Riemannian metric. We obtain area formulas for curves of that kind.

Keywords: Carnot–Carathéodory space, level set.

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English version:
Journal of Mathematical Sciences, 2015, 205:3, 335–354

Document Type: Article
UDC: 517.518.182
Received: 03.08.2012

Citation: S. G. Basalaev, “One-Dimensional Level Sets of $hc$-Differentiable Mappings of Carnot–Carathéodory Spaces”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 13:4 (2013), 16–36; J. Math. Sci., 205:3 (2015), 335–354

Citation in format AMSBIB
\Bibitem{Bas13}
\by S.~G.~Basalaev
\paper One-Dimensional Level Sets of $hc$-Differentiable Mappings of Carnot--Carath\'eodory Spaces
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2013
\vol 13
\issue 4
\pages 16--36
\mathnet{http://mi.mathnet.ru/vngu311}
\transl
\jour J. Math. Sci.
\yr 2015
\vol 205
\issue 3
\pages 335--354
\crossref{https://doi.org/10.1007/s10958-015-2251-6}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. B. Karmanova, “Graph surfaces over three-dimensional Lie groups with sub-Riemannian structure”, Siberian Math. J., 56:6 (2015), 1080–1092  mathnet  crossref  crossref  mathscinet  isi  elib
    2. M. B. Karmanova, “Three-dimensional graph surfaces on five-dimensional Carnot–Carathéodory spaces”, Siberian Math. J., 59:4 (2018), 657–676  mathnet  crossref  crossref  isi
  • Вестник Новосибирского государственного университета. Серия: математика, механика, информатика
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