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Mat. Zametki, 2003, Volume 74, Issue 3, Pages 387–395 (Mi mz272)  

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

Steiner Ratio for Manifolds

A. O. Ivanova, A. A. Tuzhilina, D. Cieslikb

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Ernst Moritz Arndt University of Greifswald

Abstract: The Steiner ratio characterizes the greatest possible deviation of the length of a minimal spanning tree from the length of the minimal Steiner tree. In this paper, estimates of the Steiner ratio on Riemannian manifolds are obtained. As a corollary, the Steiner ratio for flat tori, flat Klein bottles, and projective plane of constant positive curvature are computed.

DOI: https://doi.org/10.4213/mzm272

Full text: PDF file (215 kB)
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English version:
Mathematical Notes, 2003, 74:3, 367–374

Bibliographic databases:

UDC: 519.711.7
Received: 10.04.2000

Citation: A. O. Ivanov, A. A. Tuzhilin, D. Cieslik, “Steiner Ratio for Manifolds”, Mat. Zametki, 74:3 (2003), 387–395; Math. Notes, 74:3 (2003), 367–374

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. Ivanov, AO, “Extreme networks”, Acta Applicandae Mathematicae, 66:3 (2001), 251  crossref  mathscinet  zmath  isi  scopus  scopus
    2. 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
    3. Innami, N, “Steiner ratio for hyperbolic surfaces”, Proceedings of the Japan Academy Series A-Mathematical Sciences, 82:6 (2006), 77  crossref  mathscinet  zmath  isi  scopus  scopus
    4. Innami N., Kim B.H., Mashiko Y., Shiohama K., “The Steiner Ratio Conjecture of Gilbert-Pollak May Still Be Open”, Algorithmica, 57:4 (2010), 869–872  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    5. Ivanov A.O., Tuzhilin A.A., “The Steiner Ratio Gilbert-Pollak Conjecture Is Still Open”, Algorithmica, 62:1-2 (2012), 630–632  crossref  mathscinet  zmath  isi  scopus  scopus
    6. V. A. Mishchenko, “Estimates for the Steiner–Gromov ratio of Riemannian manifolds”, J. Math. Sci., 203:6 (2014), 833–836  mathnet  crossref  mathscinet  elib
    7. Naya Sh., Innami N., “A Comparison Theorem for Steiner Minimum Trees in Surfaces with Curvature Bounded Below”, Tohoku Math. J., 65:1 (2013), 131–157  crossref  mathscinet  zmath  isi  scopus  scopus
    8. Ivanov A.O., Tuzhilin A.A., “Branched coverings and Steiner ratio”, Int. Trans. Oper. Res., 23:5, SI (2016), 875–882  crossref  mathscinet  zmath  isi  elib  scopus
    9. 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
    10. 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  scopus
  • Математические заметки Mathematical Notes
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