Vol. 314, No. 2, 2021

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The Minkowski inequality in de Sitter space

Julian Scheuer

Vol. 314 (2021), No. 2, 425–449
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
Authors
Julian Scheuer
Cardiff University
Cardiff
Wales
United Kingdom