Geodesic
One-dimensional Gromov minimal filling problem
Sbornik. Mathematics, Tome 203 (2012) no. 5, pp. 677-726 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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A. O. Ivanov; A. A. Tuzhilin. One-dimensional Gromov minimal filling problem. Sbornik. Mathematics, Tome 203 (2012) no. 5, pp. 677-726. http://geodesic.mathdoc.fr/item/SM_2012_203_5_a2/

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