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arXiv · 2405.18501

Small volume bodies of constant width

Andrii Arman·Andriy Bondarenko·Fedor Nazarov·Andriy Prymak·Danylo Radchenko
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Abstract

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.

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Andrii Arman, Andriy Bondarenko, Fedor Nazarov, Andriy Prymak, Danylo Radchenko. 2025-01-17. Small volume bodies of constant width. https://doi.org/10.1093/imrn%2Frnaf020

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