An N-dimensional version of the Beurling-Ahlfors extension

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)321-329
Number of pages9
JournalAnnales Academiae Scientiarum Fennicae Mathematica
Volume36
Issue number1
DOIs
StatePublished - 2011

Keywords

  • Extension
  • Monotone mapping
  • Quasiconformal mapping

ASJC Scopus subject areas

  • Mathematics(all)

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