Year: 2020
Type: preprint
Abstract: For every smooth Jordan curve $γ$ and rectangle $R$ in the Euclidean plane, we show that there exists a rectangle similar to $R$ whose vertices lie on $γ$. The proof relies on Shevchishin's theorem that the Klein bottle does not admit a smooth Lagrangian embedding in $\mathbb{C}^2$.
Source: arXiv (Cornell University)
Authors: Greene, Joshua Evan, Lobb, Andrew
Institutions: Boston College, Durham University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3027973035