《苏格兰书》对乌兰第19题的否定回答

IF 5.7 1区数学 Q1 MATHEMATICS

Annals of Mathematics Pub Date : 2021-02-02 DOI:10.4007/annals.2022.195.3.5

D. Ryabogin

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引用次数: 6

摘要

我们对《苏格兰书》中的Ulam问题19给出了否定的答案，问｛是一个均匀密度的固体，它在水中的每个位置都会漂浮在一个球体上？｝假设水的密度是$1$，我们证明存在一个均匀密度$\frac｛1｝｛2｝$的严格凸旋转体$K\subet｛\mathbb R^3｝$，它不是欧几里得球，但在每个方向上都处于平衡状态。我们在所有维度$d\ge3$中证明了一个类似的结果。

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

We give a negative answer to Ulam's Problem 19 from the Scottish Book asking {\it 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 $K\subset {\mathbb R^3}$ of uniform density $\frac{1}{2}$, which is not a Euclidean ball, yet floats in equilibrium in every orientation. We prove an analogous result in all dimensions $d\ge 3$.

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来源期刊

Annals of Mathematics 数学-数学

CiteScore

9.10

自引率

2.00%

发文量

审稿时长

12 months

期刊介绍： The Annals of Mathematics is published bimonthly by the Department of Mathematics at Princeton University with the cooperation of the Institute for Advanced Study. Founded in 1884 by Ormond Stone of the University of Virginia, the journal was transferred in 1899 to Harvard University, and in 1911 to Princeton University. Since 1933, the Annals has been edited jointly by Princeton University and the Institute for Advanced Study.