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Mat. Zametki, 2003, Volume 74, Issue 5, Pages 656–668 (Mi mz298)  

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

Locally Minimal Trees in $n$-Normed Spaces

D. P. Il'yutko

M. V. Lomonosov Moscow State University

Abstract: The locally minimal trees in normed spaces $({\mathbb R}^2,\rho)$, where the unit circle $\Sigma=\{x\in{\mathbb R}^2\mid{\rho}(x)=1\}$ in the norm $\rho$ coincides with the regular $m$-gon ($m = 2n$) inscribed in the Euclidean unit circle $S^1$, are completely classified.

DOI: https://doi.org/10.4213/mzm298

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English version:
Mathematical Notes, 2003, 74:5, 619–629

Bibliographic databases:

UDC: 514.77+519.711.72+517.982.22
Received: 03.09.2001
Revised: 21.04.2003

Citation: D. P. Il'yutko, “Locally Minimal Trees in $n$-Normed Spaces”, Mat. Zametki, 74:5 (2003), 656–668; Math. Notes, 74:5 (2003), 619–629

Citation in format AMSBIB
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\paper Locally Minimal Trees in $n$-Normed Spaces
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\transl
\jour Math. Notes
\yr 2003
\vol 74
\issue 5
\pages 619--629
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. P. Il'yutko, “Branching extremals of the functional of $\lambda$-normed length”, Sb. Math., 197:5 (2006), 705–726  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    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. 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  scopus
    4. 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
    5. 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
    6. M. Yu. Zhitnaya, “Modelirovanie optimalnykh setei s pomoschyu sharnirnykh mekhanizmov”, Fundament. i prikl. matem., 22:6 (2019), 95–122  mathnet
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