Inverse curvature flows in asymptotically Robertson Walker spaces |
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Authors: | Heiko Kröner |
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Institution: | Mathematisches Institut, Abteilung für Reine Mathematik, Albert-Ludwigs-Universität, Eckerstr. 1, 79104 Freiburg, Germany |
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Abstract: | In this paper we consider inverse curvature flows in a Lorentzian manifold N which is the topological product of the real numbers with a closed Riemannian manifold and equipped with a Lorentzian metric having a future singularity so that N is asymptotically Robertson Walker. The flow speeds are future directed and given by where F is a homogeneous degree one curvature function of class of the principal curvatures, i.e. the n-th root of the Gauss curvature. We prove longtime existence of these flows and that the flow hypersurfaces converge to smooth functions when they are rescaled with a proper factor which results from the asymptotics of the metric. |
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