The rectangular peg problem

IF 5.7 1区数学 Q1 MATHEMATICS Annals of Mathematics Pub Date : 2020-05-19 DOI:10.4007/annals.2021.194.2.4

J. Greene, A. Lobb

引用次数: 16

Abstract

For every smooth Jordan curve $\gamma$ and rectangle $R$ in the Euclidean plane, we show that there exists a rectangle similar to $R$ whose vertices lie on $\gamma$. The proof relies on Shevchishin's theorem that the Klein bottle does not admit a smooth Lagrangian embedding in $\mathbb{C}^2$.

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矩形钉问题

对于欧几里得平面上的每一个光滑Jordan曲线$\gamma$和矩形$R$，我们证明了存在一个类似于$R$的矩形，其顶点位于$\gamma$上。该证明依赖于Shevchishin的定理，即克莱因瓶不允许在$\mathbb{C}^2$中有光滑的拉格朗日嵌入。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.

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