RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Subscription

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Tr.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Tr., 2011, Volume 14, Number 1, Pages 70–98 (Mi mt207)  

This article is cited in 4 scientific papers (total in 4 papers)

On the generalized triangle inequality for quasimetrics induced by noncommuting vector fields

A. V. Greshnovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia

Abstract: For a sufficiently wide class of $r$-smooth basis vector fields, we obtain necessary and sufficient conditions for some anisotropic metric functions induced by these vector fields to be quasimetrics. These results are applied to the problem of the existence of a nilpotent tangent cone at a distinguished point.

Key words: canonical coordinates, generalized triangle inequality, nilpotent tangent cone, nilpotent group and algebra, vector field, quasimetric.

Full text: PDF file (344 kB)
References: PDF file   HTML file

English version:
Siberian Advances in Mathematics, 2012, 22:2, 95–114

Bibliographic databases:

Document Type: Article
UDC: 514.763+512.812.4+517.911
Received: 23.04.2009

Citation: A. V. Greshnov, “On the generalized triangle inequality for quasimetrics induced by noncommuting vector fields”, Mat. Tr., 14:1 (2011), 70–98; Siberian Adv. Math., 22:2 (2012), 95–114

Citation in format AMSBIB
\Bibitem{Gre11}
\by A.~V.~Greshnov
\paper On the generalized triangle inequality for quasimetrics induced by noncommuting vector fields
\jour Mat. Tr.
\yr 2011
\vol 14
\issue 1
\pages 70--98
\mathnet{http://mi.mathnet.ru/mt207}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2858658}
\transl
\jour Siberian Adv. Math.
\yr 2012
\vol 22
\issue 2
\pages 95--114
\crossref{https://doi.org/10.3103/S1055134412020034}


Linking options:
  • http://mi.mathnet.ru/eng/mt207
  • http://mi.mathnet.ru/eng/mt/v14/i1/p70

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. B. Karmanova, “The graphs of Lipschitz functions and minimal surfaces on Carnot groups”, Siberian Math. J., 53:4 (2012), 672–690  mathnet  crossref  mathscinet  isi
    2. A. V. Greshnov, “Proof of Gromov's theorem on homogeneous nilpotent approximation for vector fields of class $C^1$”, Siberian Adv. Math., 23:3 (2013), 180–191  mathnet  crossref  mathscinet  elib
    3. A. V. Greshnov, M. V. Tryamkin, “Exact Values of Constants in the Generalized Triangle Inequality for Some $(1,q_2)$-Quasimetrics on Canonical Carnot Groups”, Math. Notes, 98:4 (2015), 694–698  mathnet  crossref  crossref  mathscinet  isi  elib
    4. A. V. Arutyunov, A. V. Greshnov, “$(q_1,q_2)$-quasimetric spaces. Covering mappings and coincidence points”, Izv. Math., 82:2 (2018), 245–272  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Математические труды Siberian Advances in Mathematics
    Number of views:
    This page:313
    Full text:82
    References:23
    First page:5

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019