RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






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


Izv. RAN. Ser. Mat., 2002, Volume 66, Issue 5, Pages 33–82 (Mi izv402)  

This article is cited in 6 scientific papers (total in 6 papers)

Branching geodesics in normed spaces

A. O. Ivanov, A. A. Tuzhilin

M. V. Lomonosov Moscow State University

Abstract: We study branching extremals of length functionals on normed spaces. This is a natural generalization of the Steiner problem in normed spaces. We obtain criteria for a network to be extremal under deformations that preserve the topology of networks as well as under deformations with splitting. We discuss the connection between locally shortest networks and extremal networks. In the important particular case of the Manhattan plane, we get a criterion for a locally shortest network to be extremal.

DOI: https://doi.org/10.4213/im402

Full text: PDF file (5101 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2002, 66:5, 905–948

Bibliographic databases:

UDC: 514.77+519.176
MSC: 05C35, 90C35, 68R10
Received: 22.05.2001

Citation: A. O. Ivanov, A. A. Tuzhilin, “Branching geodesics in normed spaces”, Izv. RAN. Ser. Mat., 66:5 (2002), 33–82; Izv. Math., 66:5 (2002), 905–948

Citation in format AMSBIB
\Bibitem{IvaTuz02}
\by A.~O.~Ivanov, A.~A.~Tuzhilin
\paper Branching geodesics in normed spaces
\jour Izv. RAN. Ser. Mat.
\yr 2002
\vol 66
\issue 5
\pages 33--82
\mathnet{http://mi.mathnet.ru/izv402}
\crossref{https://doi.org/10.4213/im402}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1965936}
\zmath{https://zbmath.org/?q=an:1112.90377}
\transl
\jour Izv. Math.
\yr 2002
\vol 66
\issue 5
\pages 905--948
\crossref{https://doi.org/10.1070/IM2002v066n05ABEH000402}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33748479074}


Linking options:
  • http://mi.mathnet.ru/eng/izv402
  • https://doi.org/10.4213/im402
  • http://mi.mathnet.ru/eng/izv/v66/i5/p33

    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. H. Edelsbrunner, A. Ivanov, R. Karasev, “Current Open Problems in Discrete and Computational Geometry”, Model. i analiz inform. sistem, 19:5 (2012), 5–17  mathnet
    2. I. L. Laut, Z. N. Ovsyannikov, “The type of minimal branching geodesics defines the norm in a normed space”, J. Math. Sci., 203:6 (2014), 799–805  mathnet  crossref  mathscinet
    3. E. A. Zaval'nyuk, “Local structure of minimal networks in A. D. Alexandrov spaces”, Moscow University Mathematics Bulletin, 69:5 (2014), 220–224  mathnet  crossref  mathscinet
    4. I. L. Laut, “Reconstruction of norm by geometry of minimal networks”, Moscow University Mathematics Bulletin, 71:2 (2016), 84–87  mathnet  crossref  mathscinet  isi
    5. Ivanov A.O., Tuzhilin A.A., “Minimal Networks: a Review”, Advances in Dynamical Systems and Control, Studies in Systems Decision and Control, 69, eds. Sadovnichiy V., Zgurovsky M., Springer Int Publishing Ag, 2016, 43–80  crossref  mathscinet  zmath  isi  scopus
    6. I. L. Laut, “Correlation between the norm and the geometry of minimal networks”, Sb. Math., 208:5 (2017), 684–706  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:340
    Full text:150
    References:48
    First page:1

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