Convex floating bodies of equilibrium
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- by D. I. Florentin, C. Schütt, E. M. Werner and N. Zhang PDF
- Proc. Amer. Math. Soc. 150 (2022), 3037-3048 Request permission
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 $\frac {1}{2}$. For $n=3$, this result is due to Falconer.References
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Additional Information
- D. I. Florentin
- Affiliation: Department of Mathematics, Bar-Ilan University, Israel
- MR Author ID: 949547
- ORCID: 0000-0003-1044-0977
- Email: danflorentin@gmail.com
- C. Schütt
- Affiliation: Mathematisches Seminar, Christian-Albrechts University of Kiel, Ludewig-Meyn-Strasse 4, 24098 Kiel, Germany
- Email: schuett@math.uni-kiel.de
- E. M. Werner
- Affiliation: Department of Mathematics, Case Western Reserve University, Cleveland, Ohio 44106
- MR Author ID: 252029
- ORCID: 0000-0001-9602-2172
- Email: elisabeth.werner@case.edu
- N. Zhang
- Affiliation: School of Mathematics and Statistics, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan, Hubei 430074, China
- MR Author ID: 1049706
- ORCID: 0000-0002-2854-3790
- Email: nzhang2@hust.edu.cn
- Received by editor(s): November 1, 2020
- Received by editor(s) in revised form: May 29, 2021
- Published electronically: April 7, 2022
- Additional Notes: The third author was partially supported by NSF grant DMS-1811146 and by a Simons Fellowship
- Communicated by: Deane Yang
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 3037-3048
- MSC (2020): Primary 52A20
- DOI: https://doi.org/10.1090/proc/15697
- MathSciNet review: 4428887