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Sbornik: Mathematics, 2006, Volume 197, Issue 5, Pages 705–726
DOI: https://doi.org/10.1070/SM2006v197n05ABEH003775
(Mi sm1559)
 

This article is cited in 10 scientific papers (total in 10 papers)

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

D. P. Il'yutko

M. V. Lomonosov Moscow State University
References:
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.
Received: 22.03.2005
Russian version:
Matematicheskii Sbornik, 2006, Volume 197, Number 5, Pages 75–98
DOI: https://doi.org/10.4213/sm1559
Bibliographic databases:
UDC: 514.77+519.711.72+517.982.22
MSC: Primary 05C35; Secondary 05C05, 46B20, 90C35
Language: English
Original paper language: Russian
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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Linking options:
  • https://www.mathnet.ru/eng/sm1559
  • https://doi.org/10.1070/SM2006v197n05ABEH003775
  • https://www.mathnet.ru/eng/sm/v197/i5/p75
  • This publication is cited in the following 10 articles:
    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:469
    Russian version PDF:206
    English version PDF:7
    References:80
    First page:2
     
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