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arXiv · 2607.08338

Rigidity in the planar Ulam floating body problem with perimetral densities $\sigma=\tfrac18,\tfrac38$ under central symmetry

Oleg Asipchuk·Maksim Kosmakov·Pavel Zatitskii
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Abstract

We prove that the only planar, centrally symmetric, strictly convex body $K\subset\mathbb{R}^2$ with $C^1$ boundary that floats in equilibrium in every orientation for the perimetral densities $\sigma=\tfrac18$ or $\sigma=\tfrac38$ is a disk.

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Oleg Asipchuk, Maksim Kosmakov, Pavel Zatitskii. 2026-07-09. Rigidity in the planar Ulam floating body problem with perimetral densities $\sigma=\tfrac18,\tfrac38$ under central symmetry. https://arxiv.org/abs/2607.08338

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