Equilateral dimension of the planar Banach--Mazur compactum

Tomasz Kobos; Konrad Swanepoel

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arXiv · 2503.21478

Equilateral dimension of the planar Banach--Mazur compactum

Tomasz Kobos·Konrad Swanepoel

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Abstract

We prove that there are arbitrarily large equilateral sets of planar and symmetric convex bodies in the Banach--Mazur distance. The order of the size of these $d$-equilateral sets asymptotically matches the bounds of the size of maximum-size $d$-separated sets (determined by Bronstein in 1978), showing that our construction is essentially optimal.

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BibTeX RIS

Tomasz Kobos, Konrad Swanepoel. 2025-03-27. Equilateral dimension of the planar Banach--Mazur compactum. https://arxiv.org/abs/2503.21478

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