A Class Of Curvature Flows Expanded By Support Function And Curvature Function In The Euclidean Space And Hyperbolic Space

In this paper, we first consider a class of expanding flows of closed, smooth, star-shaped hypersurface in Euclidean space $\mathbb{R}^{n+1}$ with speed $u^\alpha f^{-\beta}$, where $u$ is the support function of the hypersurface, $f$ is a smooth, symmetric, homogenous of degree one, positive function of the principal curvatures of the hypersurface on a convex cone. For $\alpha \le 0