A note on inverse mean curvature flow in cosmological spacetimes

作者：Kroener Heiko

来源：Mathematische Nachrichten, 2014, 287(2-3): 290-296.

DOI：10.1002/mana.201200342

• Lorentzian manifold
• cosmological spacetime
• general relativity
• inverse mean curvature flow

In [12] Gerhardt proves longtime existence for the inversemean 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] 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.

• 出版日期2014-2