BZ Seminar in Analysis: Gerhard Huisken (University of Tübingen)

A fully non-linear flow with surgeries for 2-convex hyper-surfaces

The lecture describes joint work with Simon Brendle on the motion of closed hyper surfaces in a Riemannian manifold, on which the sum of any two principal curvatures is positive at all points. We exhibit a fully non-linear, parabolic choice of deformation law that preserves this curvature condition and allows only neck-like singularities which can be overcome by finitely many surgeries. The lecture explains the analytical techniques involved and sharp geometric conclusions made possible by this flow. 

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