This article is cited in 7 papers

A Continuity Criterion for Steiner-Type Ratios in the Gromov–Hausdorff Space

A. C. Pahkomova<sup>ab

a</sup> M. V. Lomonosov Moscow State University
^b Delone Laboratory of Discrete and Computational Geometry, P. G. Demidov Yaroslavl State University

Abstract: A criterion for the continuity of the Steiner ratio, the Steiner subratio, and the Steiner–Gromov ratio in the space of all compact metric spaces with the Gromov–Hausdorff metric is obtained. It is also proved that these functions are upper semicontinuous.

Keywords: Steiner ratio, Steiner subratio, Steiner–Gromov ratio, Gromov–Hausdorff metric, Gromov–Hausdorff space, minimal filling, Steiner minimal tree.

UDC: 515.124+519.176

Received: 18.01.2013
Revised: 18.11.2013

DOI: 10.4213/mzm10253

 English version: Mathematical Notes, 2014, 96:1, 130–139

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