The Gromov – Hausdorff distances to simplexes
https://doi.org/10.22405/2226-8383-2019-20-2-108-122
Abstract
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.
About the Authors
D. S. Grigor’evRussian Federation
Alexander Olegovich Ivanov
Russian Federation
Alexey Augustinovich Tuzhilin
Russian Federation
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Review
For citations:
Grigor’ev D.S., Ivanov A.O., Tuzhilin A.A. The Gromov – Hausdorff distances to simplexes. Chebyshevskii Sbornik. 2019;20(2):108-122. (In Russ.) https://doi.org/10.22405/2226-8383-2019-20-2-108-122
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