Curvature flows without singularities

我们希望研究像平均曲率流这样的曲率流的解。具体地说，我们想要研究在时间依赖域上作为适当图给出的解。结果表明，上面的图不仅满足曲率流，而且在弱意义下也满足下面区域的边界.我们希望研究是否存在主曲率在下面的几何意义下有界的解，并将其应用于Neumann边界条件.我们还想给出完全非线性曲率流的存在性证明，并找到平均曲率流的新的图解平移解。

We wish to investigate solutions to curvature flows like mean curvature flow. In particular, we want to study solutions that are given as proper graphs over time dependent domains. It turns out that not only the graphs above fulfil a curvature flow but in a weak sense also the boundaries of the domains below.We wish to investigate, whether there exist solutions with principal curvatures above bounded in terms of the geometry below and apply this to Neumann boundary conditions. We also want to give an existence proof for fully nonlinear curvature flows and find new graphical translating solutions to mean curvature flow.