"Dynamic Stability of the Mean Curvature Flow and Surface area Preserving Mean Curvature FLow"

Abstract: The mean curvature flow (MCF) is a natural geometric flow of hypersurfaces. Under MCF, the hypersurfaces move by surface tension and the surface area decreases most rapidly along the flow. It is often given as a model for soap films which tend to converge to a minimal surface (surface with least area). In this talk we will discuss the dynamic stability of the MCF and surface area preserving mean curvature flow (SAP-MCF) starting from a class of initial hypersurfaces which are close to a sphere in weak sense (but not necessarily convex). Classic results for both flows are proved when the initial hypersurfaces are strictly convex. This talk is based on joint works with Zheng Huang (CUNY) and Natasa Sesum (Rutgers).