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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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1601.06710.pdf (Preprint), 544KB
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### Creators

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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: -
Rev. Method: -
Identifiers: arXiv: 1601.06710
URI: http://arxiv.org/abs/1601.06710
Degree: -

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