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Gromov-Hausdorff Geometry of Metric Trees

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arxiv 2412.18888 v1 pith:ZG7X22HI submitted 2024-12-25 math.MG

A.O. Ivanov , I.N. Mikhailov , A.A. Tuzhilin This is my paper · ORCID
classification math.MG
keywords metrictreetreesclasssubsetsubsetsallowscondition
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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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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Gromov-Hausdorff distance and Jung constant of finite-dimensional normed spaces

    math.MG 2026-07 reject novelty 7.0 of 10

    The paper gives a Gromov–Hausdorff lower bound via the relative Jung constant (sound) but its stronger Jung-constant version relies on an impossible normalization step.

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