Analysis Seminar

We will discuss the mean curvature flow of $n$-dimensional submanifolds in $\mathbb{R}^{n+k}$ satisfying a pinching condition $|A|^2 < c|H|^2$ introduced by Andrews and Baker (2010). For suitable constants $c$, these flows resemble flows of convex hypersurfaces and two-convex hypersurfaces, studied in Huisken (1984) and Huisken-Sinestrari (2009). After observing that singularity formation always appears to be codimension one, we will discuss a quantitative estimate for this behavior. Then we will discuss several applications.