One-Dimensional Level Sets of $hc$-Differentiable Mappings of Carnot--Carath\'eodory Spaces
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 13 (2013) no. 4, pp. 16-36
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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.
Keywords:
Carnot–Carathéodory space, level set.
@article{VNGU_2013_13_4_a1,
author = {S. G. Basalaev},
title = {One-Dimensional {Level} {Sets} of $hc${-Differentiable} {Mappings} of {Carnot--Carath\'eodory} {Spaces}},
journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
pages = {16--36},
publisher = {mathdoc},
volume = {13},
number = {4},
year = {2013},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VNGU_2013_13_4_a1/}
}
TY - JOUR AU - S. G. Basalaev TI - One-Dimensional Level Sets of $hc$-Differentiable Mappings of Carnot--Carath\'eodory Spaces JO - Sibirskij žurnal čistoj i prikladnoj matematiki PY - 2013 SP - 16 EP - 36 VL - 13 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VNGU_2013_13_4_a1/ LA - ru ID - VNGU_2013_13_4_a1 ER -
%0 Journal Article %A S. G. Basalaev %T One-Dimensional Level Sets of $hc$-Differentiable Mappings of Carnot--Carath\'eodory Spaces %J Sibirskij žurnal čistoj i prikladnoj matematiki %D 2013 %P 16-36 %V 13 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/VNGU_2013_13_4_a1/ %G ru %F VNGU_2013_13_4_a1
S. G. Basalaev. One-Dimensional Level Sets of $hc$-Differentiable Mappings of Carnot--Carath\'eodory 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/