Homeomorphisms of the Heisenberg group preserving BMO

Riikka Korte, Niko Marola, Olli Saari

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We provide a new geometric proof of Reimann's theorem characterizing quasiconformal mappings as the ones preserving functions of bounded mean oscillation. While our proof is new already in the Euclidean spaces, it is applicable in Heisenberg groups as well as in more general stratified nilpotent Carnot groups.

Original languageEnglish
Pages (from-to)175-182
Number of pages8
JournalARCHIV DER MATHEMATIK
Volume106
Issue number2
DOIs
Publication statusPublished - Feb 2016
MoE publication typeA1 Journal article-refereed

Keywords

  • Carnot group
  • Function of bounded mean oscillation
  • Heisenberg group
  • Metric space
  • Quasiconformal mapping
  • Stratified group
  • QUASI-CONFORMAL MAPPINGS
  • MAPS
  • QUASICONFORMALITY
  • SPACES

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