On the evolution of hypersurfaces along their inverse spacetime mean curvature

2022/08/11 by Gerhard Huisken, Huisken, Gerhard, Markus Wolff +1
Mathematics · Physics and Astronomy · #35D40 #35Q75 (Secondary) #53C (Primary) #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2208.05709

openalex publication_date 2022/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct weak solutions for the evolution of hypersurfaces along their inverse space-time mean curvature in asymptotically flat maximal initial data sets. As the speed of the new flow is given by a space-time invariant, it can detect both future- and past-trapped apparent horizons. The weak solution extends concepts developed by Huisken-Ilmanen for inverse mean curvature flow and by Moore for inverse null mean curvature flow.

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