Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvature
  We prove convergence results for expanding curvature flows in the Euclidean
and hyperbolic space. The flow speeds have the form $F^{-p}$, where $p>1$ and
$F$ is a positive, strictly monotone and 1-homogeneous curvature function. In
particular this class includes the mean curvature $F=H$. We prove that a
certain initial pinching condition is preserved and the properly rescaled
hypersurfaces converge smoothly to the unit sphere. We show that an example due
to Andrews-McCoy-Zheng can be used to construct strictly convex initial
hypersurfaces, for which the inverse mean curvature flow to the power $p>1$
loses convexity, justifying the necessity to impose a certain pinching
condition on the initial hypersurface.
