Mean curvature flow with surgery

Abstract: 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 R$^3$, 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.

analysis of PDEsdifferential geometry

Audience: researchers in the topic

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NCTS international Geometric Measure Theory seminar

Series comments: We envisage an event built around virtual presentations on progress in geometric measure theory by external speakers. Every researcher is free to register as a participant and thus gain access to a virtual facility which is complete with lobby, lecture hall, and areas with boards for discussion. Thus, it shall recreate the exchange possibilities found at international conferences.

Focus: regularity and singularity theories for submanifolds of Riemannian manifolds and some of its applications.

Frequency: one presentation every other month.

Registration: required for new participants, go to the seminar website (allow at least one working day for processing).

Virtual venue: HyHyve space NCTS iGMT seminar (only for registered participants, opened one hour before the events).

You might want to consult the description of the premises and instructions.

Former organiser: Guido De Philippis (till March 2022).

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