Equilateral dimension of the planar Banach-Mazur compactum
Kobos, T. & Swanepoel, K.
(2025).
Equilateral dimension of the planar Banach-Mazur compactum.
Proceedings of the American Mathematical Society,
153(10), 4423 - 4436.
https://doi.org/10.1090/proc/17323
(2025).
Equilateral dimension of the planar Banach-Mazur compactum.
Proceedings of the American Mathematical Society,
153(10), 4423 - 4436.
https://doi.org/10.1090/proc/17323
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
