Krümmungsprobleme

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We consider invers, non-scale-invariant curvature flows in the sphere and in Lorentzian manifolds. In case the ambient space is the sphere we consider inverse as well as direct curvature flows and want to prove that the inverse flows converge to an equator and the direct flows contract to a point. After an appropriate rescalation both flows should converge to a geodesic sphere.In globally hyperbolic Lorentzian manifolds we analyze inverse curvature flows and want to prove that the flows create a foliation of a future end provided the manifold satisfies some fairly mild assumptions. In case the manifold offers more special properties like an appropriate asymptotic behaviour near the singularity we would like to show that the flows are rescalable such that the rescaled flows converge.