Geodesic
Steiner Ratio for Manifolds
Matematičeskie zametki, Tome 74 (2003) no. 3, pp. 387-395

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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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     author = {A. O. Ivanov and A. A. Tuzhilin and D. Cieslik},
     title = {Steiner {Ratio} for {Manifolds}},
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A. O. Ivanov; A. A. Tuzhilin; D. Cieslik. Steiner Ratio for Manifolds. Matematičeskie zametki, Tome 74 (2003) no. 3, pp. 387-395. http://geodesic.mathdoc.fr/item/MZM_2003_74_3_a6/