On the extension of quasisymmetric maps
Copyright policy )On the extension of quasisymmetric maps
Quasisymmetric mappings as well as \(\varepsilon\)-power-quasisymmetric mappings are considered. It is proved that such mappings have a continuous extension from a given \(c\)-sturdy set to the Euclidean \(n\)-space. Moreover, the above extension is \(C\varepsilon\)-power-quasisymmetric for some \(C\) depending only on \(c\) and \(n\). In particular, the result mentioned above holds for quasiconformal mappings with small dilatation.
- Aalto University Finland
- Novosibirsk State University Russian Federation
SETS, ta111, extension, PLANE, BILIPSCHITZ, sturdy, quasiconformal mappings, Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations, extension to \(\mathbb R^n\), quasisymmetric mappings, Power quasisymmetric
SETS, ta111, extension, PLANE, BILIPSCHITZ, sturdy, quasiconformal mappings, Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations, extension to \(\mathbb R^n\), quasisymmetric mappings, Power quasisymmetric
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).1 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!