The Steiner–Gromov ratio of a metric space X characterizes the ratio of the minimal filling weight to the minimal spanning tree length for a finite subset of X. It is proved that the Steiner–Gromov ratio of an arbitrary Riemannian manifold does not exceed the Steiner–Gromov ratio of the Euclidean space of the same dimension.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 18, No. 2, pp. 119–124, 2013.
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Mishchenko, V.A. Estimates for the Steiner–Gromov Ratio of Riemannian Manifolds. J Math Sci 203, 833–836 (2014). https://doi.org/10.1007/s10958-014-2173-8
- Riemannian Manifold
- Span Tree
- Steiner Tree
- Weighted Graph