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arXiv · 2412.18888

Gromov-Hausdorff Geometry of Metric Trees

A. O. Ivanov·I. N. Mikhailov·A. A. Tuzhilin
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Abstract

In this paper, we study metric trees, without any finiteness restrictions. For subsets of such trees, a condition that guarantees that the Hausdorff and Gromov--Hausdorff distances from the subset to the entire metric tree are the same is obtained. This result allows to construct a new class of shortest geodesics (in the proper class of all metric spaces) connecting such subset of a metric tree with the tree itself. In particular, the technique elaborated is demonstrated on subsets of the real line.

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A. O. Ivanov, I. N. Mikhailov, A. A. Tuzhilin. 2024-12-25. Gromov-Hausdorff Geometry of Metric Trees. https://arxiv.org/abs/2412.18888

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