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 $\mathbb{C}^2$.
Citation
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
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