A continuity criterion for Steiner-type ratios in the Gromov-Hausdorff space

DOI10.1134/S0001434614070128zbMath1312.05043OpenAlexW1965974385MaRDI QIDQ2342345

A. S. Pakhomova

Publication date: 11 May 2015

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434614070128

zbMATH Keywords

Steiner minimal treeminimal fillingSteiner ratioGromov-Hausdorff metricGromov-Hausdorff spaceSteiner-Gromov ratioSteiner subratio

Mathematics Subject Classification ID

Trees (05C05) Extremal problems in graph theory (05C35) Metric spaces, metrizability (54E35) Combinatorial aspects of finite geometries (05B25) Distance in graphs (05C12)

Related Items (6)

The functions that do not change types of minimal fillings ⋮ On inductive and inverse limits of systems of compact metric spaces and applications ⋮ Classification of metric spaces whose Steiner-Gromov ratio is equal to one ⋮ Steiner ratio for Hadamard surfaces of curvature at most \(k < 0\) ⋮ Steiner type ratios of Gromov-Hausdorff space ⋮ Branched coverings and Steiner ratio

Cites Work

• Estimates of Steiner subratio and Steiner-Gromov ratio
• Two new examples of sets without medians and centers
• Filling Riemannian manifolds
• The Steiner ratio
• An example of nonexistence of a Steiner point in a Banach space
• One-dimensional Gromov minimal filling problem
• On minimal graphs containing $n$ given points
• Steiner Minimal Trees
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