Small volume bodies of constant width
Fuente:
arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912283483963392 |
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| author | Arman, Andrii Bondarenko, Andriy Nazarov, Fedor Prymak, Andriy Radchenko, Danylo |
| author_facet | Arman, Andrii Bondarenko, Andriy Nazarov, Fedor Prymak, Andriy Radchenko, Danylo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_18501 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Small volume bodies of constant width Arman, Andrii Bondarenko, Andriy Nazarov, Fedor Prymak, Andriy Radchenko, Danylo Metric Geometry 52A20, 52A40, 28A75, 49Q20 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. |
| title | Small volume bodies of constant width |
| topic | Metric Geometry 52A20, 52A40, 28A75, 49Q20 |
| url | https://arxiv.org/abs/2405.18501 |