Quermassintegral preserving curvature flow in Hyperbolic space

Abstract

We consider the quermassintegral preserving flow of closed h-convex hypersurfaces in hyperbolic space with the speed given by any positive power of a smooth symmetric, strictly increasing, and homogeneous of degree one function f of the principal curvatures which is inverse concave and has dual f* approaching zero on the boundary of the positive cone. We prove that if the initial hypersurface is h-convex, then the solution of the flow becomes strictly h-convex for t > 0, the flow exists for all time and converges to a geodesic sphere exponentially in the smooth topology. Show more