| Abstract: |
Mean curvature flow (MCF) is the negative gradient flow of volume, so it is hoped that MCF can be useful for constructing minimal submanifolds. When finite-time singularities occur, a `blow-up’ procedure produces ancient solutions, which are solutions to MCF defined for all negative time. In this sense, finite-time singularities are modeled on ancient solutions. In this talk, I will explore recent development in ancient solutions in the case where the submanifolds are Lagrangian — a natural class of half-dimensional submanifolds generalizing the plane curves. |