2012/11/21 by Heiko Kröner, Kröner, Heiko
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #math.DG
paper · pdf · doi:10.48550/arxiv.1211.5046
arxiv created 2012/11/21 · openalex publication_date 2012/11/21 · arxiv updated 2012/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In [8] Gerhardt proves longtime existence for the inverse mean curvature flow in globally hyperbolic Lorentzian manifolds with compact Cauchy hypersurface, which satisfy three main structural assumptions: a strong volume decay condition, a mean curvature barrier condition and the timelike convergence condition. Furthermore, it is shown in [8] that the leaves of the inverse mean curvature flow provide a foliation of the future of the initial hypersurface. We show that this result persists, if we generalize the setting by leaving the mean curvature barrier assumption out. For initial hypersurfaces with sufficiently large mean curvature we can weaken the timelike convergence condition to a physically relevant energy condition.