The Minkowski inequality in de Sitter space

Julian Scheuer

Vol. 314 (2021), No. 2, 425–449

DOI: 10.2140/pjm.2021.314.425

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. We employ a locally constrained inverse mean curvature flow to prove a properly defined analogue in the Lorentzian de Sitter space.

Keywords

Minkowski inequality, locally constrained curvature flow, de Sitter space

Mathematical Subject Classification

Primary: 53C21, 53E10

Secondary: 39B62

Milestones

Received: 1 June 2020

Revised: 12 July 2021

Accepted: 5 August 2021

Published: 10 November 2021