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Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2016, Number 2, Pages 53–56 (Mi vmumm139)  

Short notes

Reconstruction of norm by geometry of minimal networks

I. L. Laut

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The inverse problem to the Steiner minimal tree searching problem in a normed space is studied. Namely, let a normed space be given and all Steiner minimal trees be known in this space. The problem is to describe all norms with the same minimal Steiner trees for all finite boundary sets as determined in a given space. The paper presents a review of known results on the question and announces the uniqueness of the set of Steiner minimal trees for any two-dimensional space with a strongly convex and differentiable norm.

Key words: Fermat point, Steiner tree, normed space, norm.

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English version:
Moscow University Mathematics Bulletin, 2016, 71:2, 84–87

Bibliographic databases:

UDC: 514.77+519.176
Received: 07.09.2015

Citation: I. L. Laut, “Reconstruction of norm by geometry of minimal networks”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2016, no. 2, 53–56; Moscow University Mathematics Bulletin, 71:2 (2016), 84–87

Citation in format AMSBIB
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