Stability of non-compact manifolds under curvature flows

点击翻译按钮获取中文摘要

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.