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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
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
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
Linking options:
https://www.mathnet.ru/eng/sm7777https://doi.org/10.1070/SM2012v203n05ABEH004239 https://www.mathnet.ru/eng/sm/v203/i5/p65
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Abstract page: | 1330 | Russian version PDF: | 442 | English version PDF: | 20 | References: | 107 | First page: | 69 |
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