This article is cited in 14 papers

Steiner Ratio for Manifolds

A. O. Ivanov^a, A. A. Tuzhilin^a, D. Cieslik<sup>b

a</sup> 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.

UDC: 519.711.7

Received: 10.04.2000

DOI: 10.4213/mzm272

 English version: Mathematical Notes, 2003, 74:3, 367–374

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