Small volume bodies of constant width

Andrii Arman, Andriy Bondarenko, Fedor Nazarov, Andriy Prymak, Danylo Radchenko

Published 2024-05-28Version 1

For every large enough $n$, we explicitly construct a body of constant width $2$ that has volume less than $0.9^n \text{Vol}(\mathbb{B}^{n}$), where $\mathbb{B}^{n}$ is the unit ball in $\mathbb{R}^{n}$. This answers a question of O.~Schramm.