Premium
A note on inverse mean curvature flow in cosmological spacetimes
Author(s) -
Kröner Heiko
Publication year - 2014
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201200342
Subject(s) - hypersurface , mean curvature flow , mathematics , mean curvature , curvature , inverse , mathematical analysis , convergence (economics) , initial value problem , flow (mathematics) , willmore energy , geometry , economics , economic growth
In [12][C. Gerhardt, 2008] 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 [12][C. Gerhardt, 2008] 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.