Geodesic
One-Dimensional Level Sets of $hc$-Differentiable Mappings of Carnot–Carathéodory Spaces
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 13 (2013) no. 4, pp. 16-36 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Mots-clés : Carnot–Carathéodory space
Keywords: level set. 
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S. G. Basalaev. One-Dimensional Level Sets of $hc$-Differentiable Mappings of Carnot–Carathéodory Spaces. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 13 (2013) no. 4, pp. 16-36. http://geodesic.mathdoc.fr/item/VNGU_2013_13_4_a1/

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