论文标题
修饰标量曲率流的渐近收敛性
Asymptotic convergence for modified scalar curvature flow
论文作者
论文摘要
在本文中，我们研究了$ \ mathbb {r}^{n+1} $的封闭式，星形的超曲面的流动，并使用速度$ r^ασ_2^{1/2}，$ n $σ_2^{1/2} $是标量曲率的正常平方根，$ nise $ a iS $ geq 2，$ n is $ a iS $ reptir y restry otter的距离，以及我们证明流动一直存在，并保留了星形。此外，在归一化之后，我们表明该流量将指数迅速收敛到以原点为中心的球体。当$α<2时，给出上述收敛的反例。
In this paper, we study the flow of closed, starshaped hypersurfaces in $\mathbb{R}^{n+1}$ with speed $r^ασ_2^{1/2},$ where $σ_2^{1/2}$ is the normalized square root of the scalar curvature, $α\geq 2,$ and $r$ is the distance from points on the hypersurface to the origin. We prove that the flow exists for all time and the starshapedness is preserved. Moreover, after normalization, we show that the flow converges exponentially fast to a sphere centered at origin. When $α<2,$ a counterexample is given for the above convergence.
