×

Bi-Lipschitz pieces between manifolds. (English) Zbl 1342.28007

Let \(X\) and \(Y\) be Ahlfors \(s\)-regular, linearly locally contractible, complete, oriented, topological \(d\)-manifolds, \(s>0\), \(d\in \mathbb{N}\), and \(Y\) has \(d\)-manifold weak tangents. Let \(I\) be a dyadic \(0\)-cube in \(X\), and \(z: I\to Y\) a Lipschitz map. Then, for every \(\varepsilon>0\), there are measurable subsets \(E_{j}\subset I\), \(j=1, 2, \dots, n\), such that \(z|_{E_j}\) is bi-Lipschitz, and \(\left|z\left(I\setminus\bigcup_{j=1}^{n}E_{j}\right)\right|<\varepsilon|I|\).

MSC:

28A75 Length, area, volume, other geometric measure theory
51F99 Metric geometry
30L10 Quasiconformal mappings in metric spaces
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.