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arXiv · 1607.06655

Geometry of Compact Metric Space in Terms of Gromov-Hausdorff Distances to Regular Simplexes

Alexander O. Ivanov·Alexey A. Tuzhilin
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Abstract

In the present paper we investigate geometric characteristics of compact metric spaces, which can be described in terms of Gromov-Hausdorff distances to simplexes, i.e., to finite metric spaces such that all their nonzero distances are equal to each other. It turns out that these Gromov-Hausdorff distances depend on some geometrical characteristics of finite partitions of the compact metric spaces; some of the characteristics can be considered as a natural analogue of the lengths of edges of minimum spanning trees. As a consequence, we constructed an unexpected example of a continuum family of pairwise non-isometric finite metric spaces with the same distances to all simplexes.

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Alexander O. Ivanov, Alexey A. Tuzhilin. 2016-07-22. Geometry of Compact Metric Space in Terms of Gromov-Hausdorff Distances to Regular Simplexes. https://arxiv.org/abs/1607.06655

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