Asymptotic convergence for modified scalar curvature flow
Asymptotic convergence for modified scalar curvature flow
In this paper, we study the flow of closed, starshaped hypersurfaces in $\mathbb{R}^{n+1}$ with speed $r^\alpha\sigma_2^{1/2},$ where $\sigma_2^{1/2}$ is the normalized square root of the scalar curvature, $\alpha\geq 2,$ and $r$ is the distance from points on the hypersurface to the origin. We prove that the flow exists for all …