PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 150, Number 7, July 2022, Pages 3037-3048 https://doi.org/10.1090/proc/15697 Article electronically published on April 7, 2022 CONVEX FLOATING BODIES OF EQUILIBRIUM

D. I. Florentin; C. Schütt; E. M. Werner; N. Zhang

doi:10.1090/proc/15697

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 150, Number 7, July 2022, Pages 3037-3048 https://doi.org/10.1090/proc/15697 Article electronically published on April 7, 2022 CONVEX FLOATING BODIES OF EQUILIBRIUM

D. I. Florentin
, C. Schütt
, E. M. Werner
, N. Zhang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

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 1/2. For n = 3, this result is due to Falconer.

Original language	English
Pages (from-to)	3037-3048
Number of pages	12
Journal	Proceedings of the American Mathematical Society
Volume	150
Issue number	7
DOIs	https://doi.org/10.1090/proc/15697
State	Published - 1 Jul 2022

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Publisher Copyright:
© 2022 American Mathematical Society

Keywords

floating bodies
Ulam Problem

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Florentin, D. I., Schütt, C., Werner, E. M., & Zhang, N. (2022). PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 150, Number 7, July 2022, Pages 3037-3048 https://doi.org/10.1090/proc/15697 Article electronically published on April 7, 2022 CONVEX FLOATING BODIES OF EQUILIBRIUM. Proceedings of the American Mathematical Society, 150(7), 3037-3048. https://doi.org/10.1090/proc/15697

Florentin, D. I. ; Schütt, C. ; Werner, E. M. et al. / PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 150, Number 7, July 2022, Pages 3037-3048 https://doi.org/10.1090/proc/15697 Article electronically published on April 7, 2022 CONVEX FLOATING BODIES OF EQUILIBRIUM. In: Proceedings of the American Mathematical Society. 2022 ; Vol. 150, No. 7. pp. 3037-3048.

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Florentin, DI, Schütt, C, Werner, EM & Zhang, N 2022, 'PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 150, Number 7, July 2022, Pages 3037-3048 https://doi.org/10.1090/proc/15697 Article electronically published on April 7, 2022 CONVEX FLOATING BODIES OF EQUILIBRIUM', Proceedings of the American Mathematical Society, vol. 150, no. 7, pp. 3037-3048. https://doi.org/10.1090/proc/15697

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 150, Number 7, July 2022, Pages 3037-3048 https://doi.org/10.1090/proc/15697 Article electronically published on April 7, 2022 CONVEX FLOATING BODIES OF EQUILIBRIUM. / Florentin, D. I.; Schütt, C.; Werner, E. M. et al.
In: Proceedings of the American Mathematical Society, Vol. 150, No. 7, 01.07.2022, p. 3037-3048.

Research output: Contribution to journal › Article › peer-review

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PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 150, Number 7, July 2022, Pages 3037-3048 https://doi.org/10.1090/proc/15697 Article electronically published on April 7, 2022 CONVEX FLOATING BODIES OF EQUILIBRIUM

Abstract

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