论文标题
渐近圆锥形更高的跨跨越自我碎片和自我膨胀者的唯一性
Uniqueness of Asymptotically Conical Higher Codimension Self-Shrinkers and Self-Expanders
论文作者
论文摘要
令$ c $为$ m $ dimensional锥体沉浸在$ \ mathbb {r}^{n+m} $中。在本文中，我们表明，如果$ f：m^m \ rightarrow \ mathbb {r}^{n+m} $是一种适当沉浸式沉浸式平均曲率自我冲突器，它是顺利地渐近到$ c $的，那么它是唯一的，并且与单位倍增为$ c $。此外，如果$ f_1 $和$ f_2 $是自我膨胀的人，它们都会顺畅地散布到$ c $，它们的分离速度快于$ρ^{ - m-1} e^{ - ρ^2/4} $，在hausdorff计量中，然后$ f_1 $ f_1 $和$ f_2 $ coinciess $ f_1 $ f_2 $ cosins co。
Let $C$ be an $m$-dimensional cone immersed in $\mathbb{R}^{n+m}$. In this paper, we show that if $F:M^m \rightarrow \mathbb{R}^{n+m}$ is a properly immersed mean curvature flow self-shrinker which is smoothly asymptotic to $C$, then it is unique and converges to $C$ with unit multiplicity. Furthermore, if $F_1$ and $F_2$ are self-expanders that both converge to $C$ smoothly asymptotically and their separation decreases faster than $ρ^{-m-1}e^{-ρ^2/4}$ in the Hausdorff metric, then the images of $F_1$ and $F_2$ coincide.
