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Sibirskii Matematicheskii Zhurnal, 2008, Volume 49, Number 1, Pages 67–86 (Mi smj1823)  
This article is cited in 4 scientific papers (total in 4 papers)

Differentiability of horizontal curves in Carnot–Carathéodory quasispaces

A. V. Greshnov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Full-text PDF (381 kB) Citations (4)
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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.
Keywords: Carnot–Carathéodory space, nilpotent group, tangent cone, quasimetric, differentiability, curve.
Received: 05.09.2006
Revised: 13.09.2007
English version:
Siberian Mathematical Journal, 2008, Volume 49, Issue 1, Pages 53–68
DOI: https://doi.org/10.1007/s11202-008-0006-z
Bibliographic databases:
UDC: 514.763.22+517.518.15+514.752.8
Language: Russian
Citation: A. V. Greshnov, “Differentiability of horizontal curves in Carnot–Carathéodory quasispaces”, Sibirsk. Mat. Zh., 49:1 (2008), 67–86; Siberian Math. J., 49:1 (2008), 53–68
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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