Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvature

Heiko Kröner, Julian Scheuer

Published 2017-03-21Version 1

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, homogeneous of degree $1$ and concave 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.