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September 2021 The rectangular peg problem
Joshua Greene, Andrew Lobb
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Ann. of Math. (2) 194(2): 509-517 (September 2021). DOI: 10.4007/annals.2021.194.2.4

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 the theorem of Shevchishin and Nemirovski that the Klein bottle does not admit a smooth Lagrangian embedding in $\mathbb{C}^2$.

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Joshua Greene. Andrew Lobb. "The rectangular peg problem." Ann. of Math. (2) 194 (2) 509 - 517, September 2021. https://doi.org/10.4007/annals.2021.194.2.4

Information

Published: September 2021
First available in Project Euclid: 21 December 2021

Digital Object Identifier: 10.4007/annals.2021.194.2.4

Subjects:
Primary: 51F99 , 53D12

Keywords: aspect ratio , inscribed rectangles , Jordan curve , Lagrangian surface , symplectic geometry

Rights: Copyright © 2021 Joshua Evan Greene and Andrew Lobb

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Vol.194 • No. 2 • September 2021
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