Mean curvature flow with surgeries of two-convex hypersurfaces
speaker: Carlo Sinestrari (Università di Roma "Tor Vergata")abstract: We describe a procedure (developed in collaboration with G. Huisken) about the continuation after the singular time of the mean curvature flow of hypersurfaces based on a surgery procedure. The method has analogies with the Hamilton-Perelman construction for the Ricci flow. Compared with the notions of weak solutions available in the literature on the mean curvature flow, the flow with surgeries has the advantage of an easier analysis of the possible topological changes of the evolving manifold. We are able to define such a flow for hypersurfaces of the euclidean space which are two-convex (i.e. such that the sum of the two smallest principal curvatures is positive everywhere). As a corollary, we obtain a topological classification of these manifolds.
timetable:
Tue 30 Jun, 11:30 - 12:30, Aula Dini
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