Locally constrained inverse curvature flow and an Alexandrov-Fenchel inequality in de Sitter space

Abstract

The long-time existence and convergence are shown for the locally constrained inverse curvature flow of compact spacelike convex hypersurfaces in de Sitter space. As an application, the Alexandrov-Fenchel inequality between the quermassintegrals A0 and An−1 is established in view of their opposite monotonicity along the considered flow. With the help of the dual relationship, a geometric inequality concerning quermassintegrals of convex hypersurfaces in a hyperbolic space of even dimension follows.