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Paper

#### A new version of Brakke's local regularity theorem

##### Fulltext (public)

1601.06710.pdf

(Preprint), 544KB

1601.06710v2.pdf

(Preprint), 530KB

##### Supplementary Material (public)

There is no public supplementary material available

##### Citation

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

Cite as: http://hdl.handle.net/11858/00-001M-0000-0029-6F9C-9

##### 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.