The Minkowski inequality in de Sitter space

TL;DR

This paper extends the classical Minkowski inequality to de Sitter space using a specialized inverse mean curvature flow, providing a Lorentzian analogue of a fundamental geometric inequality.

Contribution

It introduces a novel method employing a locally constrained inverse mean curvature flow to prove a Minkowski-type inequality in de Sitter space.

Findings

Established a Minkowski inequality in de Sitter space

Developed a new flow technique for Lorentzian geometry

Provided geometric bounds analogous to Euclidean results

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.