Convex floating bodies of equilibrium

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 nn-dimensional convex bodies whose relative density to water is 12\frac {...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2022-07, Vol.150 (7), p.3037-3048
Hauptverfasser: Florentin, D. I., Schütt, C., Werner, E. M., Zhang, N.
Format: Artikel
Sprache:eng
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Research article
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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 nn-dimensional convex bodies whose relative density to water is 12\frac {1}{2}. For n=3n=3, this result is due to Falconer.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/15697