RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Vestnik Moskov. Univ. Ser. 1. Mat. Mekh.: Year: Volume: Issue: Page: Find

 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.

Full text: PDF file (288 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 514.77+519.176

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
\Bibitem{Lau16} \by I.~L.~Laut \paper Reconstruction of norm by geometry of minimal networks \jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh. \yr 2016 \issue 2 \pages 53--56 \mathnet{http://mi.mathnet.ru/vmumm139} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3637818} \transl \jour Moscow University Mathematics Bulletin \yr 2016 \vol 71 \issue 2 \pages 84--87 \crossref{https://doi.org/10.3103/S0027132216020091} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000393855500009} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84971268116}