A negative answer to Ulam's Problem 19 from the Scottish Book

• 成果类型: Article
• 署名作者: Ryabogin, Dmitry
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2022.195.3.5
• 发表日期: 2022
• 页码: 1111-1150
• 关键词: body

摘要

We give a negative answer to Ulam's Problem 19 from the Scottish Book asking is a solid of uniform density which will float in water in every position a sphere? Assuming that the density of water is 1, we show that there exists a strictly convex body of revolution K subset of R-3 of uniform density 1/2, which is not a Euclidean ball, yet floats in equilibrium in every orientation. We prove an analogous result in all dimensions d >= 3.