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Almost graphical hypersurfaces become graphical under mean curvature flow

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Lahiri,  Ananda
Geometric Measure Theory, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1505.00543.pdf
(Preprint), 479KB

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Citation

Lahiri, A. (in press). Almost graphical hypersurfaces become graphical under mean curvature flow. Communications in Analysis and Geometry.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0026-CA5B-3
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.