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

2026/07/20 by Henry Adams, Semeon A. Bogatyi, Florian Frick +5
Mathematics · #math.MG

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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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