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Matematicheskie Zametki, 2003, Volume 74, Issue 3, Pages 387–395
DOI: https://doi.org/10.4213/mzm272 (Mi mzm272) 		 
This article is cited in 14 scientific papers (total in 14 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
Full-text PDF (215 kB) Citations (14)
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DOI: https://doi.org/10.4213/mzm272
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.
Received: 10.04.2000
English version:
Mathematical Notes, 2003, Volume 74, Issue 3, Pages 367–374
DOI: https://doi.org/10.1023/A:1026106802540
Bibliographic databases:
UDC: 519.711.7
Language: Russian
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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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математические заметки Mathematical Notes
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