Equilateral dimension of the planar Banach--Mazur compactum
Metric Geometry
2026-01-12 v2 Functional Analysis
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 -equilateral sets asymptotically matches the bounds of the size of maximum-size -separated sets (determined by Bronstein in 1978), showing that our construction is essentially optimal.
Keywords
Cite
@article{arxiv.2503.21478,
title = {Equilateral dimension of the planar Banach--Mazur compactum},
author = {Tomasz Kobos and Konrad Swanepoel},
journal= {arXiv preprint arXiv:2503.21478},
year = {2026}
}