FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2013, VOLUME 18, NUMBER 2, PAGES 119-124

**Estimates for the Steiner--Gromov ratio of Riemannian manifolds**

V. A. Mishchenko

Abstract

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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.

Location: http://mech.math.msu.su/~fpm/eng/k13/k132/k13209h.htm

Last modified: January 7, 2014