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  Almost graphical hypersurfaces become graphical under mean curvature flow

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

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0026-CA5B-3 Version Permalink: http://hdl.handle.net/21.11116/0000-0002-F65C-2
Genre: Paper

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1505.00543.pdf (Preprint), 479KB
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 Creators:
Lahiri, Ananda1, Author              
Affiliations:
1Geometric Measure Theory, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_1753352              

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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.

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 Dates: 2015-05-0420152016
 Publication Status: Accepted / In Press
 Pages: 33 pages
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1505.00543
URI: http://arxiv.org/abs/1505.00543
 Degree: -

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Title: Communications in Analysis and Geometry
Source Genre: Journal
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Publ. Info: Hong Kong : International Press
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: - Identifier: ISSN: 1019-8385
CoNE: /journals/resource/954925586286