论文标题
通过$ \ mathbb {r}^2 $中曲率的亚物种关键力量对古代流的分类
Classification of ancient flows by sub-affine-critical powers of curvature in $\mathbb{R}^2$
论文作者
论文摘要
我们将关闭的凸$α$ -Curve缩短的缩短流量$α\ leq \ frac {1} {3} $。此外，我们还表明，封闭的凸平平滑有限熵$α$ curve缩短了$ \ frac {1} {3} {3} <α$是一个收缩的圆圈。归一化后，满足上述条件的古老流程将指数迅速地汇聚到后向无穷大的光滑封闭凸的收缩器。特别是，当$α= \ frac {1} {k^2-1} $带有$ 3 \ leq k \ in \ mathbb {n} $中时，圆形圆形收缩器具有非平凡的雅各比田，但是古老的流量并没有沿Jacobi领域进化。
We classify closed convex $α$-curve shortening flows for sub-affine-critical powers $α\leq \frac{1}{3}$. In addition, we show that closed convex smooth finite entropy $α$-curve shortening flows with $\frac{1}{3}<α$ is a shrinking circle. After normalization, the ancient flows satisfying the above conditions converge exponentially fast to smooth closed convex shrinkers at the backward infinity. In particular, when $α=\frac{1}{k^2-1}$ with $3\leq k \in \mathbb{N}$, the round circle shrinker has non-trivial Jacobi fields, but the ancient flows do not evolve along the Jacobi fields.
