论文标题
关于方形钉问题
On the square peg problem
论文作者
论文摘要
我们表明，如果$γ$是$ \ mathbb {r}^2 $中的Jordan曲线，它接近$ C^2 $ Jordan Curve $β$ in $ \ MATHBB {r}^2 $，则$γ$包含一个刻有刻有的广场。特别是，如果$κ> 0 $是$β$的最大无符号曲率，并且有一个$ f $ $γ$的图$ f $，到$ | | | | f（x）-x ||的图像$γ$ to $β$的图像<\ frac {1} {10κ} $和$ f \circγ$具有绕组数量$ 1 $，然后$γ$具有刻有正侧长度的正方形。
We show that if $γ$ is a Jordan curve in $\mathbb{R}^2$ which is close to a $C^2$ Jordan curve $β$ in $\mathbb{R}^2$, then $γ$ contains an inscribed square. In particular, if $κ> 0$ is the maximum unsigned curvature of $β$ and there is a map $f$ from the image of $γ$ to the image of $β$ with $||f(x) - x|| < \frac{1}{10 κ}$ and $f \circ γ$ having winding number $1$, then $γ$ has an inscribed square of positive sidelength.
