Reifenberg Parameterizations for Sets with Holes
نویسنده
چکیده
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 β1(x, r). In particular, it applies in the locally Ahlfors-regular case to provide very big pieces of bi-Lipschitz images of R. AMS classification. 28A75, 49Q05, 49Q20, 49K99.
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