RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
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



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






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


Mat. Sb., 2001, Volume 192, Number 6, Pages 31–50 (Mi msb571)  

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

Differential calculus on the space of Steiner minimal trees in Riemannian manifolds

A. O. Ivanov, A. A. Tuzhilin

M. V. Lomonosov Moscow State University

Abstract: It is proved that the length of a minimal spanning tree, the length of a Steiner minimal tree, and the Steiner ratio regarded as functions of finite subsets of a connected complete Riemannian manifold have directional derivatives in all directions. The derivatives of these functions are calculated and some properties of their critical points are found. In particular, a geometric criterion for a finite set to be critical for the Steiner ratio is found. This criterion imposes essential restrictions on the geometry of the sets for which the Steiner ratio attains its minimum, that is, the sets on which the Steiner ratio of the boundary set is equal to the Steiner ratio of the ambient space.

DOI: https://doi.org/10.4213/sm571

Full text: PDF file (325 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2001, 192:6, 823–841

Bibliographic databases:

UDC: 514.77+512.816.4+517.924.8
MSC: Primary 05C05; Secondary 05C10, 05C35, 51M16, 57M15
Received: 21.08.2000

Citation: A. O. Ivanov, A. A. Tuzhilin, “Differential calculus on the space of Steiner minimal trees in Riemannian manifolds”, Mat. Sb., 192:6 (2001), 31–50; Sb. Math., 192:6 (2001), 823–841

Citation in format AMSBIB
\Bibitem{IvaTuz01}
\by A.~O.~Ivanov, A.~A.~Tuzhilin
\paper Differential calculus on the space of Steiner minimal trees in Riemannian manifolds
\jour Mat. Sb.
\yr 2001
\vol 192
\issue 6
\pages 31--50
\mathnet{http://mi.mathnet.ru/msb571}
\crossref{https://doi.org/10.4213/sm571}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1860140}
\zmath{https://zbmath.org/?q=an:1032.05034}
\transl
\jour Sb. Math.
\yr 2001
\vol 192
\issue 6
\pages 823--841
\crossref{https://doi.org/10.1070/SM2001v192n06ABEH000571}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000171221500010}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0035538768}


Linking options:
  • http://mi.mathnet.ru/eng/msb571
  • https://doi.org/10.4213/sm571
  • http://mi.mathnet.ru/eng/msb/v192/i6/p31

    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. A. O. Ivanov, A. A. Tuzhilin, “Uniqueness of Steiner minimal trees on boundaries in general position”, Sb. Math., 197:9 (2006), 1309–1340  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. E. A. Zavalnyuk, “Steiner ratio for the Hadamard surfaces of curvature at most $k<0$”, J. Math. Sci., 203:6 (2014), 777–788  mathnet  crossref  mathscinet
    3. E. I. Stepanova, “Directional derivative of the weight of a minimal filling in Riemannian manifolds”, Moscow University Mathematics Bulletin, 70:1 (2015), 14–18  mathnet  crossref  mathscinet  elib
    4. A. O. Ivanov, A. A. Tuzhilin, “Analiticheskie deformatsii minimalnykh setei”, Fundament. i prikl. matem., 21:5 (2016), 159–180  mathnet
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:260
    Full text:71
    References:24
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2018