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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



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






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


Sbornik: Mathematics, 2017, Volume 208, Issue 5, Pages 684–706
DOI: https://doi.org/10.1070/SM8751
(Mi sm8751)
 

Correlation between the norm and the geometry of minimal networks

I. L. Laut

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
References:
Abstract: The paper is concerned with the inverse problem of the minimal Steiner network problem in a normed linear space. Namely, given a normed space in which all minimal networks are known for any finite point set, the problem is to describe all the norms on this space for which the minimal networks are the same as for the original norm. We survey the available results and prove that in the plane a rotund differentiable norm determines a distinctive set of minimal Steiner networks. In a two-dimensional space with rotund differentiable norm the coordinates of interior vertices of a nondegenerate minimal parametric network are shown to vary continuously under small deformations of the boundary set, and the turn direction of the network is determined.
Bibliography: 15 titles.
Keywords: Fermat point, minimal Steiner network, minimal parametric network, normed space, norm.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00378-а
Ministry of Education and Science of the Russian Federation НШ-7962.2016.1
This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 16-01-00378-a) and the Programme for the Support of Leading Scientific Schools of the President of the Russian Federation (grant no. НШ-7962.2016.1).
Received: 08.06.2016 and 18.10.2016
Russian version:
Matematicheskii Sbornik, 2017, Volume 208, Number 5, Pages 103–128
DOI: https://doi.org/10.4213/sm8751
Bibliographic databases:
UDC: 514.77+519.176+517.982.22
MSC: Primary 05C35, 51M16; Secondary 05C05, 52B05
Language: English
Original paper language: Russian
Citation: I. L. Laut, “Correlation between the norm and the geometry of minimal networks”, Mat. Sb., 208:5 (2017), 103–128; Sb. Math., 208:5 (2017), 684–706
Citation in format AMSBIB
\Bibitem{Lau17}
\by I.~L.~Laut
\paper Correlation between the norm and the geometry of minimal networks
\jour Mat. Sb.
\yr 2017
\vol 208
\issue 5
\pages 103--128
\mathnet{http://mi.mathnet.ru/sm8751}
\crossref{https://doi.org/10.4213/sm8751}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3646488}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2017SbMat.208..684L}
\elib{https://elibrary.ru/item.asp?id=29106642}
\transl
\jour Sb. Math.
\yr 2017
\vol 208
\issue 5
\pages 684--706
\crossref{https://doi.org/10.1070/SM8751}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000405686500004}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85025096974}
Linking options:
  • https://www.mathnet.ru/eng/sm8751
  • https://doi.org/10.1070/SM8751
  • https://www.mathnet.ru/eng/sm/v208/i5/p103
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:975
    Russian version PDF:108
    English version PDF:17
    References:53
    First page:12
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024