Gromov-Hausdorff Geometry of Metric Trees
Metric Geometry
2024-12-30 v1
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.
Cite
@article{arxiv.2412.18888,
title = {Gromov-Hausdorff Geometry of Metric Trees},
author = {A. O. Ivanov and I. N. Mikhailov and A. A. Tuzhilin},
journal= {arXiv preprint arXiv:2412.18888},
year = {2024}
}
Comments
10 pages, 0 figures