Reifenberg Parameterizations for Sets with Holes

Reifenberg Parameterizations for Sets with Holes
Author :
Publisher : American Mathematical Soc.
Total Pages : 114
Release :
ISBN-10 : 9780821853108
ISBN-13 : 0821853104
Rating : 4/5 (104 Downloads)

Book Synopsis Reifenberg Parameterizations for Sets with Holes by : Guy David

Download or read book Reifenberg Parameterizations for Sets with Holes written by Guy David and published by American Mathematical Soc.. This book was released on 2012 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors 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 $\beta_1(x,r)$. In particular, it applies in the locally Ahlfors-regular case to provide very big pieces of bi-Lipschitz images of $\mathbb R^d$.


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