论文标题
在$ \ mathbb r^2 $中，曲率的流量的古老解决方案
Ancient solutions for flow by powers of the curvature in $\mathbb R^2$
论文作者
论文摘要
我们构建了$κ^α$的新型嵌入式凸的古老解决方案，$ \ Mathbb r^2 $，$α\ in（\ frac12,1）$，位于两个平行线之间。使用此解决方案，我们将$κ^α$的所有凸旧解决方案分类为$ \ Mathbb r^2 $，以$α\ in（\ frac23,1）$。此外，我们表明，$κ^α$的任何非紧凑型凸凸的古老解决方案$ \ mathbb r^2 $，$α\ in（\ frac12,1）$都必须是翻译解决方案。
We construct a new compact convex embedded ancient solution of the $κ^α$ flow in $\mathbb R^2$, $α\in(\frac12,1)$ that lies between two parallel lines. Using this solution we classify all convex ancient solutions of the $κ^α$ flow in $\mathbb R^2$, for $α\in(\frac23,1)$. Moreover, we show that any non-compact convex embedded ancient solution of the $κ^α$ flow in $\mathbb R^2$, $α\in(\frac12,1)$ must be a translating solution.
