Communications in Analysis and Geometry
Volume 25 (2017)
Almost graphical hypersurfaces become graphical under mean curvature flow
Pages: 589 – 623
Consider a mean curvature flow of hypersurfaces in Euclidean space, that is initially graphical inside a cylinder. There exists a period of time during which the flow is graphical inside the cylinder of half the radius. Here we prove a lower bound on this period depending on the Lipschitz-constant of the initial graphical representation. This is used to deal with a mean curvature flow that lies in a slab and is initially graphical inside a cylinder except for a small set.We show that such a flow will become graphical inside the cylinder of half the radius. The proofs are mainly based on White’s regularity theorem.
Paper received on 2 June 2015.