We study continuously hc-differentiable mappings from a Carnot–Carathéodory space ℳ such that dim Hgℳ = dimTgℳ − 1 = N for every g ∈ ℳ to an Euclidean N-dimensional space with the property that the hc-differential of the mapping is surjective. We prove that the level set of such a mapping is a curve with Hausdorff dimension 2 in the sub-Riemannian metric. We obtain area formulas for curves of that kind. Bibliography: 17 titles.
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Translated from Vestnik Novosibirskogo Gosudarstvennogo Universiteta: Seriya Matematika, Mekhanika, Informatika 13, No. 4, 2013, pp. 16-36.
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Basalaev, S.G. One-Dimensional Level Sets of hc-Differentiable Mappings of Carnot–Carathéodory Spaces. J Math Sci 205, 335–354 (2015). https://doi.org/10.1007/s10958-015-2251-6
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DOI: https://doi.org/10.1007/s10958-015-2251-6