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  A new version of Brakke's local regularity theorem

Lahiri, A. (in preparation). A new version of Brakke's local regularity theorem.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0029-6F9C-9 Version Permalink: http://hdl.handle.net/21.11116/0000-0002-F65D-1
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1601.06710.pdf (Preprint), 544KB
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 Creators:
Lahiri, Ananda1, Author              
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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 an integral Brakke flow $(\mu_t)$, $t\in [0,T]$ inside some ball in Euclidean space. If $\mu_{0}$ has small height, its measure does not deviate too much from that of a plane and if $\mu_{T}$ is non-empty, than Brakke's local regularity theorem yields that $(\mu_t)$ is actually smooth and graphical inside a smaller ball for times $t\in (C,T-C)$ for some constant $C$. Here we extend this result to times $t\in (C,T)$. The main idea is to prove that a Brakke flow that is initially locally graphical with small gradient will remain graphical for some time.

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 Dates: 2016-01-25
 Publication Status: Not specified
 Pages: 39 pages
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: arXiv: 1601.06710
URI: http://arxiv.org/abs/1601.06710
 Degree: -

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