ABSTRACT We study the regularity of the parametrizations of level surfaces of continuously horizo... more ABSTRACT We study the regularity of the parametrizations of level surfaces of continuously horizontally differentiable real-valued mappings of Carnot groups. Equations that describe a regular hypersurface in terms of parametrizations are obtained.
ABSTRACT We obtain the Poincaré inequality for the equiregular Carnot-Carathéodory spaces spanned... more ABSTRACT We obtain the Poincaré inequality for the equiregular Carnot-Carathéodory spaces spanned by vector fields with Hölder class derivatives.
We study the approximate differentiability of measurable mappings of Carnot--Carath\'eodory s... more We study the approximate differentiability of measurable mappings of Carnot--Carath\'eodory spaces. We show that the approximate differentiability almost everywhere is equivalent to the approximate differentiability along the basic horizontal vector fields almost everywhere. As a geometric tool we prove the generalization of Rashevsky--Chow theorem for $C^1$-smooth vector fields. The main result of the paper extends theorems on approximate differentiability proved by Stepanoff (1923, 1925) and Whitney (1951) in Euclidean spaces and by Vodopyanov (2000) on Carnot groups.
ABSTRACT We study the regularity of the parametrizations of level surfaces of continuously horizo... more ABSTRACT We study the regularity of the parametrizations of level surfaces of continuously horizontally differentiable real-valued mappings of Carnot groups. Equations that describe a regular hypersurface in terms of parametrizations are obtained.
ABSTRACT We obtain the Poincaré inequality for the equiregular Carnot-Carathéodory spaces spanned... more ABSTRACT We obtain the Poincaré inequality for the equiregular Carnot-Carathéodory spaces spanned by vector fields with Hölder class derivatives.
We study the approximate differentiability of measurable mappings of Carnot--Carath\'eodory s... more We study the approximate differentiability of measurable mappings of Carnot--Carath\'eodory spaces. We show that the approximate differentiability almost everywhere is equivalent to the approximate differentiability along the basic horizontal vector fields almost everywhere. As a geometric tool we prove the generalization of Rashevsky--Chow theorem for $C^1$-smooth vector fields. The main result of the paper extends theorems on approximate differentiability proved by Stepanoff (1923, 1925) and Whitney (1951) in Euclidean spaces and by Vodopyanov (2000) on Carnot groups.
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Papers by Sergey Basalaev