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arXiv · 2103.12497

Corona Decompositions for Parabolic Uniformly Rectifiable Sets

Simon Bortz·John Hoffman·Steve Hofmann·José Luis Luna Garcia·Kaj Nyström
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Abstract

We prove that parabolic uniformly rectifiable sets admit (bilateral) corona decompositions with respect to regular Lip(1,1/2) graphs. Together with our previous work, this allows us to conclude that if $\Sigma\subset\mathbb{R}^{n+1}$ is parabolic Ahlfors-David regular, then the following statements are equivalent. (1) $\Sigma$ is parabolic uniformly rectifiable. (2) $\Sigma$ admits a corona decomposition with respect to regular Lip(1,1/2) graphs. (3) $\Sigma$ admits a bilateral corona decomposition with respect to regular Lip(1,1/2) graphs. (4) $\Sigma$ is big pieces squared of regular Lip(1,1/2) graphs.

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Simon Bortz, John Hoffman, Steve Hofmann, José Luis Luna Garcia, Kaj Nyström. 2021-03-23. Corona Decompositions for Parabolic Uniformly Rectifiable Sets. https://arxiv.org/abs/2103.12497

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