Uniqueness of Flotation and Buoyancy Surfaces for Convex Polytopes
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915999958171648 |
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| author | Dann, Susanna Herscovici, Orli Myroshnychenko, Sergii |
| author_facet | Dann, Susanna Herscovici, Orli Myroshnychenko, Sergii |
| contents | We prove that a convex polytope $P \subset \mathbb{R}^d$, $d \ge 2$, of uniform density $δ\in (0,1)$ floating in a liquid of density $1$, is uniquely determined by its surface of flotation $P_{[δ]}$ whenever $δ\neq \tfrac{1}{2}$. Analogously, we show that the buoyancy surface $\mathcal{C}_δP$ of a convex polytope $P$ with prescribed density $δ\in (0,1)$ uniquely determines $P$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09776 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Uniqueness of Flotation and Buoyancy Surfaces for Convex Polytopes Dann, Susanna Herscovici, Orli Myroshnychenko, Sergii Metric Geometry Differential Geometry 52A20, 53A07, 52B11 We prove that a convex polytope $P \subset \mathbb{R}^d$, $d \ge 2$, of uniform density $δ\in (0,1)$ floating in a liquid of density $1$, is uniquely determined by its surface of flotation $P_{[δ]}$ whenever $δ\neq \tfrac{1}{2}$. Analogously, we show that the buoyancy surface $\mathcal{C}_δP$ of a convex polytope $P$ with prescribed density $δ\in (0,1)$ uniquely determines $P$. |
| title | Uniqueness of Flotation and Buoyancy Surfaces for Convex Polytopes |
| topic | Metric Geometry Differential Geometry 52A20, 53A07, 52B11 |
| url | https://arxiv.org/abs/2605.09776 |