Title: New pinching estimates for Inverse curvature flows in space forms,
Abstract: We prove new pinching estimate for the inverse curvature flow of strictly
convex hypersurfaces in the space form $N$ of constant sectional curvature
$K_N$ with speed given by $F^{-\alpha}$, where $\alpha\in (0,1]$ for $K_N=0,-1$
and $\alpha=1$ for $K_N=1$, $F$ is a smooth, symmetric homogeneous of degree
one function which is inverse concave and has dual $F_*$ approaching zero on
the boundary of the positive cone $\Gamma_+$. We show that the ratio of the
largest principal curvature to the smallest principal curvature of the flow
hypersurface is controlled by its initial value. This can be used to prove the
smooth convergence of the flow.