Title
Approximation of mean curvature flow with generic singularities by smooth flows with surgery.
Abstract
Mean curvature flow can be viewed as the ‘heat equation’ for an embedding. Indeed, on short time scales MCF will improve the regularity of the embedding. Moreover, smooth MCF is an isotopy, making it an attractive tool for answering questions concerning the geometry and topology of embeddings. Unfortunately, MCF from a compact initial condition will form singularities in finite time, posing an obstruction to the construction of isotopies. To get around this the notion of MCF with surgery was introduced, first by Huisken–Sinestrari for 2-convex hypersurfaces. I will show how to construct a MCF with surgery that approximates a mean curvature flow in which 2-convexity is only assumed on the singularities, rather than on the entire flow. This is achieved by combining recent results of Choi—Haslhofer—Hershkovits–White regarding mean-convex neighbourhoods with the 2-convex surgery procedure of Haslhofer—Kleiner At the end, I will present some topological applications.
Please note that the seminar will take place in person in room 140 of Huxley Building.