标题： 具有凸投影的曲线缩短流的奇点 显示英文标题

标题： Singularities of Curve Shortening Flow with Convex Projections

摘要： 我们证明了在$\mathbb R^n$中任何具有到某个$2$-平面的一一凸投影的闭合浸入曲线，在$\mathbb R^n$中的曲线缩短流下会发展为类型~I奇点，并且渐近变为圆形。 作为应用，我们证明了在$\mathbb R^n$中曲线缩短流的一个类似Huisken猜想的结论，表明在$\mathbb R^n$中的任何闭合浸入曲线都可以扰动为在$\mathbb R^{n+2}$中的闭合浸入曲线，该曲线在曲线缩短流下收缩为一个圆点。 显示英文摘要

摘要： We show that any closed immersed curve in $\mathbb R^n$ with a one-to-one convex projection onto some $2$-plane develops a Type~I singularity and becomes asymptotically circular under Curve Shortening flow in $\mathbb R^n$. As an application, we prove an analog of Huisken's conjecture for Curve Shortening flow in $\mathbb R^n$, showing that any closed immersed curve in $\mathbb R^n$ can be perturbed to a closed immersed curve in $\mathbb R^{n+2}$ which shrinks to a round point under Curve Shortening flow.