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Sibirskii Matematicheskii Zhurnal, 2010, Volume 51, Number 3, Pages 517–527 (Mi smj2103)  
This article is cited in 5 scientific papers (total in 5 papers)

On one class of Lipschitz vector fields in $\mathbb R^3$

A. V. Greshnovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University, Mechanics and Mathematics Department, Novosibirsk
Full-text PDF (311 kB) Citations (5)
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Abstract: Under consideration are some continuous metric functions induced by one class of Lipschitz vector fields in $\mathbb R^3$. These functions are showed to be quasimetrics within the domain of definition of the vector fields. We prove some analogs of the Rashevsky–Chow Theorem and the Ball-Box Theorem under some restriction on the class of vector fields. The methods of proofs do not use the existence of the nilpotent tangent cone.
Keywords: Lipschitz vector field, quasimetric, generalized triangle inequality, quasimetric, horizontal curve.
Received: 01.07.2009
English version:
Siberian Mathematical Journal, 2010, Volume 51, Issue 3, Pages 410–418
DOI: https://doi.org/10.1007/s11202-010-0042-3
Bibliographic databases:
Document Type: Article
UDC: 514.763+512.812.4+517.911
Language: Russian
Citation: A. V. Greshnov, “On one class of Lipschitz vector fields in $\mathbb R^3$”, Sibirsk. Mat. Zh., 51:3 (2010), 517–527; Siberian Math. J., 51:3 (2010), 410–418
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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