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Free keywords:
Mathematics, Analysis of PDEs, math.AP,Mathematics, Differential Geometry, math.DG,
Abstract:
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 inside 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.
