The Minkowski inequality in de Sitter space

Abstract

The classical Minkowski inequality in the Euclidean space provides a lower bound on the total mean curvature of a hypersurface in terms of the surface area, which is optimal on round spheres. In this paper we employ a locally constrained inverse mean curvature flow to prove a properly defined analogue in the Lorentzian de Sitter space.

21 pages

References in corpus (3)

• Alexandrov-Fenchel inequalities for convex hypersurfaces with free boundary in a ball
• The isoperimetric inequality for a minimal submanifold in Euclidean space
• Harmonic mean curvature flow and geometric inequalities

Cited by in corpus (4)

• Minkowski inequalities and constrained inverse curvature flows in warped spaces
• Blaschke-Santaló type inequalities and quermassintegral inequalities in space forms
• On the mean curvature type flow for convex capillary hypersurfaces in the ball
• The quermassintegral preserving mean curvature flow in the sphere