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Sbornik: Mathematics, 2012, Volume 203, Issue 5, Pages 677–726
DOI: https://doi.org/10.1070/SM2012v203n05ABEH004239 (Mi sm7777) 		 
This article is cited in 44 scientific papers (total in 44 papers)

One-dimensional Gromov minimal filling problem

A. O. Ivanovab, A. A. Tuzhilinba

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Laboratory of Discrete and Computational Geometry named after B. N. Delone of P. G. Demidov Yaroslavl State University
English version PDF (599 kB) Citations (44)
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DOI: https://doi.org/10.1070/SM2012v203n05ABEH004239
Abstract: The paper is devoted to a new branch in the theory of one-dimensional variational problems with branching extremals, the investigation of one-dimensional minimal fillings introduced by the authors. On the one hand, this problem is a one-dimensional version of a generalization of Gromov's minimal fillings problem to the case of stratified manifolds. On the other hand, this problem is interesting in itself and also can be considered as a generalization of another classical problem, the Steiner problem on the construction of a shortest network connecting a given set of terminals. Besides the statement of the problem, we discuss several properties of the minimal fillings and state several conjectures.
Bibliography: 38 titles.
Keywords: metric spaces, Gromov minimal fillings, Steiner minimal trees, minimal spanning trees, Steiner ratio.
Received: 04.08.2010 and 08.04.2011
Russian version:
Matematicheskii Sbornik, 2012, Volume 203, Number 5, Pages 65–118
DOI: https://doi.org/10.4213/sm7777
Bibliographic databases:
Document Type: Article
UDC: 514.774.8+515.124.4+519.176
MSC: Primary 05C12, 54E35; Secondary 05C05, 52A38
Language: English
Original paper language: Russian
Citation: A. O. Ivanov, A. A. Tuzhilin, “One-dimensional Gromov minimal filling problem”, Mat. Sb., 203:5 (2012), 65–118; Sb. Math., 203:5 (2012), 677–726
Citation in format AMSBIB
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    • This publication is cited in the following 44 articles:
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