论文标题
矩形钉问题
The Rectangular Peg Problem
论文作者
论文摘要
对于欧几里得飞机中的每条光滑的Jordan曲线$γ$和矩形$ r $，我们表明存在类似于$ r $的矩形，其顶点位于$γ$上。证据依赖于Shevchishin的定理，即Klein瓶不承认$ \ Mathbb {C}^2 $中的光滑的Lagrangian嵌入。
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 $\mathbb{C}^2$.
