ncts

Flows with surgery are a powerful method to evolve geometric shapes, and have found many important applications in geometry and topology. In this talk, I will describe a new method to establish existence of flows with surgery. In contrast to all prior constructions of flows with surgery in the literature, our new approach does not require any a priori estimates in the smooth setting. Instead, our approach uses geometric measure theory, building in particular on the work of Brakke and White. We illustrate our method in the classical setting of mean-convex surfaces in R³, thus giving a new proof of the existence results due to Brendle-Huisken and Kleiner and myself. Moreover, our new method also enables the construction of flows with surgery in situations that have been inaccessible with prior techniques, including in particular the free-boundary setting.