# Mean curvature flow with surgery for 2-convex surfaces

#### by Professor Gerhard Huisken

Institution: Max Planck Institute for Gravitational Physics, Potsdam
Date: Mon 4th September 2006
Time: 1:00 PM
Location: Russell Love Theatre, Richard Berry Building, The University of Melbourne

Abstract: We prove that closed n-dimensional hypersurfaces, n>2, in Euclidean space that have the sum of their smallest two principal curvatures everywhere positive, are diffeomorphic to a finite connected sum of copies of $S^(n-1) \times S^1$. As a corollary we show that a simply connected 3-dimensional hypersurface of positive scalar curvature in Euclidean space is a standard sphere bounding a standard ball. The proof uses mean curvature flow with surgeries following a strategy developed by Richard Hamilton for Ricciflow.