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.

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Last modified: January 7, 2014