2019/09/15 by Julian Scheuer · 2 citations
Mathematics · #Anti-de Sitter space #Computer science #Curvature #De Sitter space #De Sitter universe #Euclidean geometry #Euclidean space #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Hypersurface #Inequality #Inverse #Log sum inequality #Mathematical analysis #Mathematical physics #Mathematics #Mean curvature #Mean curvature flow #Minimal surface #Minkowski inequality #Minkowski space #Minkowski's theorem #Physics #Point processes and geometric inequalities #Pure mathematics #Quantum mechanics #Rearrangement inequality #Space (punctuation) #Surface (topology) #Universe #Upper and lower bounds #math.AP #math.DG
paper · pdf · doi:10.2140/pjm.2021.314.425
published in Pacific Journal of Mathematics 314(2), 425-449 (Mathematical Sciences Publishers) · 21 pages
arxiv created 2019/09/15 · openalex publication_date 2021/11/10 · arxiv updated 2022/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.