A note on inverse mean curvature flow in cosmological spacetimes |
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| Authors: | Heiko Kröner |
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| Affiliation: | Mathematisches Institut, Universit?t Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany |
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| Abstract: | In 12 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 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. |
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| Keywords: | Lorentzian manifold cosmological spacetime general relativity inverse mean curvature flow 35J60 53C21 53C44 53C50 58J05 |
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