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arXiv · 2607.18447

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

Henry Adams·Semeon A. Bogatyi·Florian Frick·Daniil A. Ilyukhin·Alexander O. Ivanov·Ivan N. Mikhailov·Alexey A. Tuzhilin·Anton A. Vikhrov
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Abstract

For a finite-dimensional normed space $V$ and a subset $X$ with finite Hausdorff distance from $V$, we prove that the Gromov--Hausdorff distance between $X$ and $V$ is at least the Hausdorff distance between $X$ and $V$, divided by twice the relative Jung constant of $V$. If $V$ furthermore satisfies a certain intersection property, we show a stronger result where the relative Jung constant can be replaced with its absolute version. Key words: Normed spaces, Jung constant, Hausdorff distance, Gromov--Hausdorff distance.

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Henry Adams, Semeon A. Bogatyi, Florian Frick, Daniil A. Ilyukhin, Alexander O. Ivanov, Ivan N. Mikhailov, Alexey A. Tuzhilin, Anton A. Vikhrov. 2026-07-20. Gromov-Hausdorff distance and Jung constant of finite-dimensional normed spaces. https://arxiv.org/abs/2607.18447

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