Convex floating bodies of equilibrium
We study a long standing open problem by Ulam, which is whether the Euclidean ball is the unique body of uniform density which will float in equilibrium in any direction. We answer this problem in the class of origin symmetric n-dimensional convex bodies whose relative density to water is \frac {1}{...
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| Veröffentlicht in: | Proceedings of the American Mathematical Society 2022-07, Vol.150 (7), p.3037-3048 |
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| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We study a long standing open problem by Ulam, which is whether the Euclidean ball is the unique body of uniform density which will float in equilibrium in any direction. We answer this problem in the class of origin symmetric n-dimensional convex bodies whose relative density to water is \frac {1}{2}. For n=3, this result is due to Falconer. |
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| ISSN: | 0002-9939 1088-6826 |
| DOI: | 10.1090/proc/15697 |