Wednesday, October 14, 2020 3:15 PM
Keaton Naff (Columbia)

We will discuss the mean curvature flow of $n$-dimensional submanifolds in $\mathbb{R}^{n+k}$ satisfying a pinching condition introduced by Andrews and Baker (2010): $|H| > 0$ and $|A|^2 < c|H|^2$. We will compare what is known about these flows to what is known about flows of hypersurfaces, established in the fundamental works of Huisken (1984) and Huisken-Sinestrari (2009). In particular, we will see that the singularity formation resembles the singularity formation in convex and two-convex flows in codimension one. We will then discuss a quantitative estimate for this behavior and its applications