%0 Generic
%A Kröner, Heiko
%D 2012
%F heidok:13789
%K inverser Krümmungsfluß, ARW Raum, Lorentzmannigfaltigkeit, partielle Differentialgleichungeninverse curvature flow, ARW spaces, lorentzian manifold, general relativity, partial differential equations
%R 10.11588/heidok.00013789
%T The inverse F-curvature flow in ARW spaces
%U https://archiv.ub.uni-heidelberg.de/volltextserver/13789/
%X We consider the so-called inverse $F$-curvature flow (IFCF) $dot x = -F^{-1}nu$ in ARW spaces, i.e. in Lorentzian manifolds with a special future singularity. Here, $F$ denotes a curvature function of class $(K^*)$, which is homogenous of degree one, e.g. the $n$-th root of the Gaussian curvature, and $nu$ the past directed normal. We prove existence of the IFCF for all times and convergence of the rescaled scalar solution in $C^{infty}(S_0)$ to a smooth function. Using the rescaled IFCF we maintain a transition from big crunch to big bang into a mirrored spacetime.