An N-dimensional version of the Beurling-Ahlfors extension

Leonid V. Kovalev; Jani Onninen

doi:10.5186/aasfm.2011.3620

An N-dimensional version of the Beurling-Ahlfors extension

Leonid V. Kovalev, Jani Onninen

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We extend delta-monotone quasiconformai mappings from dimension n to n + 1 while preserving both monotonicity and quasiconformality. This gives an analytic proof of the extendability of quasiconformal mappings that can be factored into bi-Lipschitz and delta-monotone mappings. In the case n = 1 our approach yields a refinement of the Beurling-Ahlfors extension.

Original language	English (US)
Pages (from-to)	321-329
Number of pages	9
Journal	Annales Academiae Scientiarum Fennicae Mathematica
Volume	36
Issue number	1
DOIs	https://doi.org/10.5186/aasfm.2011.3620
State	Published - 2011

Keywords

Extension
Monotone mapping
Quasiconformal mapping

ASJC Scopus subject areas

General Mathematics

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AB - We extend delta-monotone quasiconformai mappings from dimension n to n + 1 while preserving both monotonicity and quasiconformality. This gives an analytic proof of the extendability of quasiconformal mappings that can be factored into bi-Lipschitz and delta-monotone mappings. In the case n = 1 our approach yields a refinement of the Beurling-Ahlfors extension.

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KW - Monotone mapping

KW - Quasiconformal mapping

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An N-dimensional version of the Beurling-Ahlfors extension

Abstract

Keywords

ASJC Scopus subject areas

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