Correlation between the norm and the geometry of minimal networks

DOI10.1070/SM8751zbMath1372.05210OpenAlexW2590766813MaRDI QIDQ5369345

I. L. Laut

Publication date: 17 October 2017

Published in: Sbornik: Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/sm8751

zbMATH Keywords

minimal Steiner network problem in a normed linear space

Mathematics Subject Classification ID

Trees (05C05) Extremal problems in graph theory (05C35) Small world graphs, complex networks (graph-theoretic aspects) (05C82) Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) Inequalities and extremum problems in real or complex geometry (51M16)

Cites Work

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• Locally minimal trees in \(n\)-normed spaces
• The local Steiner problem in finite-dimensional normed spaces
• Stabilization of locally minimal trees
• Steiner minimal trees
• The Fermat--Torricelli problem in normed planes and spaces
• The type of minimal branching geodesics defines the norm in a normed space
• Location of the Fermat-Torricelli medians of three points
• Branching extremals of the functional of $ \lambda$-normed length
• An Introduction to Banach Space Theory
• The twist number of planar linear trees
• Branching geodesics in normed spaces
• Steiner Minimal Trees
• The geometry of Minkowski spaces -- a survey. I

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