Reifenberg parameterizations for sets with holes

Reifenberg parameterizations for sets with holes

Author
Guy David, Tatiana Toro
Publisher
Amer Mathematical Society
Language
English
Year
2012
Page
114
ISBN
0821853104,978-0-8218-5310-8
File Type
pdf
File Size
878.4 KiB

Extends 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 $beta1(x,r)$. In particular, it applies in the locally Ahlfors-regular case to provide very big pieces of bi-Lipschitz images of $mathbb Rd$.

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