Stability of non-compact manifolds under curvature flows

在这个项目中，我们研究了非紧流形在几何流下的演化，如平均曲率流或Ricci流。我们特别感兴趣的是解的长期行为，这些解最初接近于空间无穷远处的孤子。我们想要研究，这些解是否长时间收敛到那个孤子。这个项目的动机之一是我们想要了解这些流动在永恒解附近的长期动态行为。我们预计我们的研究将涉及基于势垒技术和考虑积分形式的熵的方法。

In this project, we study the evolution of non-compact manifolds under geometric flows like mean curvature flow or Ricci flow. We are particularly interested in the long-time behavior of solutions which are initially close to a soliton at spatial infinity. We want to study, whether these solutions converge for large times to that soliton. One of the motivations for this project is that we want to understand the long-time dynamical behavior of these flows near eternal solutions. We expect that our investigations will involve methods based on barrier techniques and on considering entropies in integral form.