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Mat. Sb., 2006, Volume 197, Number 5, Pages 75–98 (Mi msb1559)  

This article is cited in 8 scientific papers (total in 8 papers)

Branching extremals of the functional of $\lambda$-normed length

D. P. Il'yutko

M. V. Lomonosov Moscow State University

Abstract: Networks on $\lambda$-normed planes are considered, that is, on normed planes for which the unit circle is a regular $2\lambda$-gon. A geometric criterion is given for an arbitrary tree to be extremal on the $\lambda$-normed plane, where $\lambda\ne2,3,4,6$. Problems of $\lambda$-minimal (extremal) realization of an arbitrary network and of convergence of $\lambda$-extremal networks as $\lambda\to\infty$ are also considered.
Bibliography: 17 titles.

DOI: https://doi.org/10.4213/sm1559

Full text: PDF file (608 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2006, 197:5, 705–726

Bibliographic databases:

UDC: 514.77+519.711.72+517.982.22
MSC: Primary 05C35; Secondary 05C05, 46B20, 90C35
Received: 22.03.2005

Citation: D. P. Il'yutko, “Branching extremals of the functional of $\lambda$-normed length”, Mat. Sb., 197:5 (2006), 75–98; Sb. Math., 197:5 (2006), 705–726

Citation in format AMSBIB
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    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. A. G. Bannikova, D. P. Ilyutko, I. M. Nikonov, “The length of an extremal network in a normed space: Maxwell formula”, Journal of Mathematical Sciences, 214:5 (2016), 593–608  mathnet  crossref
    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. Ivanov A.O. Tuzhilin A.A., “Minimal Networks: a Review”, Advances in Dynamical Systems and Control, Studies in Systems Decision and Control, 69, ed. Sadovnichiy V. Zgurovsky M., Springer Int Publishing Ag, 2016, 43–80  crossref  mathscinet  zmath  isi  scopus
    5. E. I. Stepanova, “Bifurcations of Steiner minimal trees and minimal fillings for non-convex four-point boundaries and Steiner subratio for the Euclidean plane”, Moscow University Mathematics Bulletin, 71:2 (2016), 79–81  mathnet  crossref  mathscinet  isi
    6. I. L. Laut, “Reconstruction of norm by geometry of minimal networks”, Moscow University Mathematics Bulletin, 71:2 (2016), 84–87  mathnet  crossref  mathscinet  isi
    7. D. P. Ilyutko, I. M. Nikonov, “Extremal networks in $\lambda$-geometry, where $\lambda=3,4,6$”, Sb. Math., 208:4 (2017), 479–509  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    8. 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
  • Математический сборник Sbornik: Mathematics (from 1967)
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