Rigidity in the Planar Ulam Floating Body Problem with perimetral density $σ=\tfrac16$
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917401166086144 |
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| author | Asipchuk, Oleg Kosmakov, Maksim Zatitskii, Pavel |
| author_facet | Asipchuk, Oleg Kosmakov, Maksim Zatitskii, Pavel |
| contents | We study the two-dimensional Ulam's floating body problem for convex domains with perimetral density $σ=\tfrac16$. Using the framework of Zindler carousels, we reduce the problem to a two-dimensional dynamical system associated with an inscribed equilateral hexagon. Our main result shows that the disk is the only convex domain floating in equilibrium in every position for this perimetral density. This provides a new rigidity result for rational perimetral densities in the convex setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10330 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rigidity in the Planar Ulam Floating Body Problem with perimetral density $σ=\tfrac16$ Asipchuk, Oleg Kosmakov, Maksim Zatitskii, Pavel Metric Geometry Classical Analysis and ODEs 52A10, 52A38, 34A12, 34A26 We study the two-dimensional Ulam's floating body problem for convex domains with perimetral density $σ=\tfrac16$. Using the framework of Zindler carousels, we reduce the problem to a two-dimensional dynamical system associated with an inscribed equilateral hexagon. Our main result shows that the disk is the only convex domain floating in equilibrium in every position for this perimetral density. This provides a new rigidity result for rational perimetral densities in the convex setting. |
| title | Rigidity in the Planar Ulam Floating Body Problem with perimetral density $σ=\tfrac16$ |
| topic | Metric Geometry Classical Analysis and ODEs 52A10, 52A38, 34A12, 34A26 |
| url | https://arxiv.org/abs/2604.10330 |