论文标题
高曲率的自相似于完全非线性曲率流动的解决方案
Self-similar solutions to fully nonlinear curvature flows by high powers of curvature
论文作者
论文摘要
在本文中，我们调查了$ \ mathbb {r}^{n+1} $中严格凸出的凸起的高度凸出，它们在高曲率的高力量下缩小了一个完全非线性曲率流的大家族。当速度函数由度量$ 1 $的能力和功率大于$ 1 $的主曲线的逆凹功能给出时，我们证明唯一这样的超曲面是圆形球体。我们还证明，切片是唯一的严格凸出的自相似解，以大于或等于$ 1 $的功率或等于$ 1 $的半球$ \ mathbb {s}^{n+1} _ {n+1} $。
In this paper, we investigate closed strictly convex hypersurfaces in $\mathbb{R}^{n+1}$ which shrink self-similarly under a large family of fully nonlinear curvature flows by high powers of curvature. When the speed function is given by powers of a homogeneous of degree $1$ and inverse concave function of the principal curvatures with power greater than $1$, we prove that the only such hypersurfaces are round spheres. We also prove that slices are the only closed strictly convex self-similar solutions to such curvature flows in the hemisphere $\mathbb{S}^{n+1}_{+}$ with power greater than or equal to $1$.
