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arXiv · 0910.4869

Reifenberg Parameterizations for Sets with Holes

Guy David·Tatiana Toro
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Abstract

We extend the proof of Reifenberg's Topological Disk Theorem to allow the case of sets with holes, and give sufficient conditions on a set $E$ for the existence of a bi-Lipschitz parameterization of $E$ by a $d$-dimensional plane or smooth manifold. Such a condition is expressed in terms of square summability for the P. Jones numbers $β_1(x,r)$. In particular, it applies in the locally Ahlfors-regular case to provide very big pieces of bi-Lipschitz images of $\R^d$.

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Guy David, Tatiana Toro. 2009-10-26. Reifenberg Parameterizations for Sets with Holes. https://arxiv.org/abs/0910.4869

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