Inequalities of Alexandrov-Fenchel type for convex hypersurfaces in hyperbolic space and in the sphere

Abstract

By applying the unit normal flow to well-known inequalities in hyperbolic space Hn+1 and in the sphere Sn+1, we derive some new inequalities of Alexandrov-Fenchel type for closed convex hypersurfaces in these spaces. We also use the inverse mean curvature flow in the sphere to prove an optimal Sobolev-type inequality for closed convex hypersurfaces in the sphere. Show more