Bilipschitz extensions of maps having quasiconformal extensions
Copyright policy )Bilipschitz extensions of maps having quasiconformal extensions
We consider bilipschitz maps \(f: A\to \mathbb R^ n\), \(X\subset \mathbb R^ n\). We show that if \(n\neq 4\) and if \(f\) has a quasiconformal extension to \(\mathbb R^ n\), then \(f\) has also a bilipschitz extension to \(\mathbb R^ n\). Thus, for example, \(f\) has such an extension whenever \(X\) and \(fX\) are quasiconformal spheres. An application to the flattening theory of Lipschitz manifolds is given.
- University of Helsinki Finland
- DigiZeitschriften Germany
510.mathematics, Flatness and tameness of topological manifolds, Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations, bilipschitz extension, flattening theory, bilipschitz maps, Lipschitz manifolds, Article, quasiconformal extension
510.mathematics, Flatness and tameness of topological manifolds, Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations, bilipschitz extension, flattening theory, bilipschitz maps, Lipschitz manifolds, Article, quasiconformal extension
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