论文标题
2-convex的凸度，将孤子转换为$ \ mathbb {r}^{n+1} $中的平均曲率流量
Convexity of 2-convex translating and expanding solitons to the mean curvature flow in $\mathbb{R}^{n+1}$
论文作者
论文摘要
在本文中，受Spruck-Xiao [27]的工作的启发，部分是基于Derdziński[11]的结果，我们证明了完整的2-Convex翻译和扩展孤子曲线到平均值曲率流到$ \ Mathbb {r}^r}^{N n+1} $中的均值。更确切地说，对于$ n \ geq 3 $，我们表明任何$ n $二维完整的2-convex翻译孤子是凸的，任何$ n $ diper-n $二维的完整2-Convex自称为（严格）平均凸锥均为偶音。
In this paper, inspired by the work of Spruck-Xiao [27] and based partly on a result of Derdziński [11], we prove the convexity of complete 2-convex translating and expanding solitons to the mean curvature flow in $\mathbb{R}^{n+1}$. More precisely, for $n\geq 3$, we show that any $n$-dimensional complete 2-convex translating solitons are convex, and any $n$-dimensional complete 2-convex self-expanders asymptotic to (strictly) mean convex cones are convex.
