Variational Methods in Geometry Seminar

We study closed ancient solutions to gradient flows of elliptic functionals in Riemannian manifolds, including the mean curvature flow. As an application, we show that an ancient (arbitrarycodimension) mean curvature flow in $S^n$ with low area must be a steady geodesic sphere or a shrinking sphere. In the curve shortening case in $S^2$, our methods let us classify all ancient flows of bounded length.

This is joint work with Kyeongsu Choi.