Generic Dynamics of the Mean Curvature Flows

Explore the intricacies of mean curvature flows in this 47-minute conference talk by Jinxin Xue at BIMSA. Delve into the evolution of hypersurfaces in Euclidean space using mean curvatures as velocity fields. Examine the flow's smoothing properties and the development of singularities, with a focus on shrinkers as models for these singularities. Investigate the concept of generic mean curvature flows, introducing perturbations to initial conditions to overcome the challenge of classifying infinite shrinkers. Learn about recent work on perturbing away nonspherical and noncylindrical shrinkers, as well as the generic isolatedness of cylindrical singularities. Gain insights from a series of collaborative works with Ao Sun, advancing understanding in this complex area of mathematical physics.