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Differentiability of horizontal curves in Carnot-Carathéodory quasispaces

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Abstract

Considering a sufficiently broad class of absolutely continuous horizontal curves on Carnot-Carathéodory quasispaces, we prove that almost everywhere convergence of the horizontal coordinates of a curve to some direction at a point (an analog of the usual differentiability) implies the differentiability of the “whole” curve in the Carnot-Carathéodory sense at the same point.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    A. V. Greshnov

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  1. A. V. Greshnov
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Correspondence to A. V. Greshnov.

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Original Russian Text Copyright © 2008 Greshnov A. V.

The author was supported by the Russian Foundation for Basic Research (Grant 05-01-00482-a).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 1, pp. 67–86, January–February, 2008.

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Greshnov, A.V. Differentiability of horizontal curves in Carnot-Carathéodory quasispaces. Sib Math J 49, 53–68 (2008). https://doi.org/10.1007/s11202-008-0006-z

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  • DOI: https://doi.org/10.1007/s11202-008-0006-z

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