4/13/2012

John Head
Courant Institute

Mean curvature flow of two-convex hypersurfaces

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.