Selfsimilar solutions of the mean curvature flow

在这个关于平均曲率流的自相似解的补充项目中，我们希望找到自相似子流形在各种几何条件下的额外分类结果，并更好地理解这种子流形的存在需要什么样的约束和障碍。我们想把紧自相似子流形的结果推广到正情况，也就是说，我们想继续研究缩解l。在拉格朗日的情况下有一些很有希望的结果关于在拉格朗日子流形的情况下Futaki不变量的变体的存在这最终会给我们关于自缩解l的拓扑性质的很好的几何信息我们已经得到了一些与不变量相关的约束，但是到目前为止这些不变量还没有被完全理解它们在拉格朗日锥上是不变量而不是哈密顿锥上，这将是更可取的。我们相信这些不变量的一些改进在哈密顿锥上是不变量而在拉格朗日锥上不是。

In this supplementary project concerned with selfsimilar solutions of the mean curvature flow we want to find additional classification results for selfsimilar submanifolds under various geometric conditions and to get a better understanding of what kind of constraints and obstructions for the existence of such submanifolds are necessary. We want to extend the results in the case of compact, selfsimilar submanifolds in the positive case, i.e. we want to pursue our research on shrinking solutions L. In particular, in the Lagrangian case there are promising results concerning the existence of a variant of the Futaki invariant in case of Lagrangian submanifolds which would eventually give us nice geometric informations on the topological nature of selfshrinking solutions L. We already obtained some constraints related to invariants, but so far these invariants are not fully understood and they are invariant on the Lagrangian cone instead of the Hamiltonian cone, which would be much more desirable. We believe that there are refinements of these invariants that are invariant on the Hamiltonian cone but not on the Lagrangian cone.