# Expanding curvature flow for convex surfaces in space forms

We consider the convex surfaces expanding in space forms by powers $(0<p\leq 1)$ of a strictly monotone, homogeneous degree one function of its principal curvatures. In Euclidean case, the flow will exist for all time and converge to a round sphere after properly rescaling. In Hyperbolic case, the flow exists for all time as well, but the limit shape may not be round after rescaling. We show this by constructing a counterexample. In Spherical case, we assume that $p=1$. Then the flow exists for finite time and converges to equator. No concavity assumption on the speed function is required in all the above cases. (Joint work with Haizhong Li and Xiangfeng Wang)