Analytic Deformations of Minimal Networks

The behavior of extreme networks under deformations of their boundary sets is investigated. It is shown that analyticity of a deformation of the boundary set guarantees preservation of the network type for minimal spanning trees, minimal fillings, and so-called stable shortest trees in the Euclidean...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2020-08, Vol.248 (5), p.621-635
Main Authors: Ivanov, A. O., Tuzhilin, A. A.
Format: Article
Language:English
Subjects:
Deformation
Euclidean geometry
Euclidean space
Graph theory
Mathematics
Mathematics and Statistics
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Summary:The behavior of extreme networks under deformations of their boundary sets is investigated. It is shown that analyticity of a deformation of the boundary set guarantees preservation of the network type for minimal spanning trees, minimal fillings, and so-called stable shortest trees in the Euclidean space.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-020-04899-7