Contracting axially symmetric hypersurfaces by powers of the ${\sigma }_k$-curvature

Haizhong Li, Xianfeng Wang, Jing Wu

In this paper, we investigate the contracting curvature flow of closed, strictly convex axially symmetric hypersurfaces in ${\mathbb{R}}^{n+1}$ and ${\mathbb{S}}^{n+1}$ by ${\sigma }_k^{\alpha }$, whe…