Inverse curvature flows in hyperbolic space

Abstract

We consider inverse curvature ows in $\mathbb{H}^{n+1}$ with star-shaped initial hypersurfaces and prove that the ows 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.