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Small volume bodies of constant width

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arxiv 2405.18501 v2 pith:2I2GS5BO submitted 2024-05-28 math.MG

Andrii Arman , Andriy Bondarenko , Fedor Nazarov , Andriy Prymak , Danylo Radchenko This is my paper · ORCID
classification math.MG
keywords mathbbconstantvolumewidthanswersballbodiesbody
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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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  1. An in-depth study of ball-bodies

    math.MG 2025-05 conditional novelty 7.0 of 10

    Ball-bodies admit a near-unique duality that controls their curvature, diameter, and symmetrization behavior in Euclidean space.

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