Generic Mean Curvature Flow with Cylindrical Singularities

PDE Seminar
Tuesday, November 1, 2022 - 3:00pm for 1 hour (actually 50 minutes)
Skiles 006
Ao Sun – University of Chicago – aosun@uchicago.edu
Gong Chen

We study the local and global dynamics of mean curvature flow with cylindrical singularities. We find the most generic dynamic behavior of such singularities, and show that the singularities with the most generic dynamic behavior are robust. We also show that the most generic singularities are isolated and type-I. Among applications, we prove that the singular set structure of the generic mean convex mean curvature flow has certain patterns, and the level set flow starting from a generic mean convex hypersurface has low regularity. This is joint work with Jinxin Xue (Tsinghua University)