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Steiner Ratio for Manifolds

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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.

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, Russia

    A. O. Ivanov & A. A. Tuzhilin

  2. Mathematics and Informatics Institute, E. M. Arndt University, Greifswald, Germany

    D. Cieslik

Authors
  1. A. O. Ivanov
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  2. A. A. Tuzhilin
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  3. D. Cieslik
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Ivanov, A.O., Tuzhilin, A.A. & Cieslik, D. Steiner Ratio for Manifolds. Mathematical Notes 74, 367–374 (2003). https://doi.org/10.1023/A:1026106802540

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  • DOI: https://doi.org/10.1023/A:1026106802540

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