This article is cited in 3 papers

Estimates for the Steiner–Gromov ratio of Riemannian manifolds

V. A. Mishchenko

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

Abstract: 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.

UDC: 519.711.7

 English version: Journal of Mathematical Sciences (New York), 2014, 203:6, 833–836

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