Inverse curvature flows in hyperbolic space

Abstract

We consider inverse curvature flows in $\Hh$ with star-shaped initial hypersurfaces and prove that the flows exist for all time, and that the leaves converge to infinity, become strongly convex exponentially fast and also more and more totally umbilic. After an appropriate rescaling the leaves converge in $C^{\infty }$ to a sphere.

v5: Removed Lemma 6.12 which is false and corrected the claim that the rescaled functions in (1.12) converge to a constant; they converge to a smooth function