Geodesic
The Gromov–Hausdorff distances to simplexes
Čebyševskij sbornik, Tome 20 (2019) no. 2, pp. 108-122 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the paper geometrical characteristics of metric spaces appearing in explicit formulas for the Gromov–Hausdorff distance from this spaces to so-called simplexes, i.e., the metric spaces, all whose non-zero distances are the same. For the calculation of those distances the geometry of partitions of these spaces is important. In the case of finite metric spaces that leads to some analogues of the edges lengths of minimal spanning trees. Earlier, a similar theory was elaborated for compact metric spaces. These results are generalised to the case of an arbitrary bounded metric space, explicit formulas are obtained, and some proofs are simplified.
Keywords: Gromov–Hausdorff distance, metric geometry, metric space. 
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D. S. Grigor'ev; A. O. Ivanov; A. A. Tuzhilin. The Gromov–Hausdorff distances to simplexes. Čebyševskij sbornik, Tome 20 (2019) no. 2, pp. 108-122. http://geodesic.mathdoc.fr/item/CHEB_2019_20_2_a7/

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