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Matematicheskie Zametki, 2014, Volume 96, Issue 1, Pages 126–137
DOI: https://doi.org/10.4213/mzm10253 (Mi mzm10253) 		 
This article is cited in 7 scientific papers (total in 7 papers)

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

A. C. Pahkomovaab

a M. V. Lomonosov Moscow State University
b Delone Laboratory of Discrete and Computational Geometry, P. G. Demidov Yaroslavl State University
Full-text PDF (493 kB) Citations (7)
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DOI: https://doi.org/10.4213/mzm10253
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.
Received: 18.01.2013
Revised: 18.11.2013
English version:
Mathematical Notes, 2014, Volume 96, Issue 1, Pages 130–139
DOI: https://doi.org/10.1134/S0001434614070128
Bibliographic databases:
Document Type: Article
UDC: 515.124+519.176
Language: Russian
Citation: A. C. Pahkomova, “A Continuity Criterion for Steiner-Type Ratios in the Gromov–Hausdorff Space”, Mat. Zametki, 96:1 (2014), 126–137; Math. Notes, 96:1 (2014), 130–139
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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