Mean curvature flow of two-convex hypersurfaces

Mean curvature flow of two-convex hypersurfaces

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John Head, Courant Institute
Fine Hall 314

We describe recent progress on the mean curvature evolution of smooth, closed, two-convex hypersurfaces in Euclidean space. In this setting, there are two distinct global interpretations of the flow, namely the Huisken-Sinestrari surgery program and the well-known "weak" evolution. We explain the relationship between these two solutions, and present applications of our construction to regularity theory for mean curvature flow.