  In this paper, we first investigate the flow of convex surfaces in the space
form $\mathbb{R}^3(\kappa)~(\kappa=0,1,-1)$ expanding by $F^{-\alpha}$, where
$F$ is a smooth, symmetric, increasing and homogeneous of degree one function
of the principal curvatures of the surfaces and the power $\alpha\in(0,1]$ for
$\kappa=0,-1$ and $\alpha=1$ for $\kappa=1$. By deriving that the pinching
ratio of the flow surface $M_t$ is no greater than that of the initial surface
$M_0$, we prove the long time existence and the convergence of the flow. No
concavity assumption of $F$ is required. We also show that for the flow in
$\mathbb{H}^3$ with $\alpha\in (0,1)$, the limit shape may not be necessarily
round after rescaling.
