Krümmungsprobleme

我们考虑逆，非标度不变曲率流的领域和洛伦兹流形。在情况下的环境空间是球，我们考虑逆以及直接曲率流，并希望证明，逆流收敛到赤道和直接流合同的一个点。在全局双曲Lorentzian流形中，我们分析了逆曲率流，并希望证明，如果流形满足一些相当温和的假设，那么逆曲率流会产生一个未来端点的叶状结构。如果流形提供了更特殊的性质，例如在奇点附近的适当渐近行为，我们希望表明流是可重标度的，使得重标度流收敛。

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.