Homeomorphisms of the Heisenberg group preserving BMO

Riikka Korte; Niko Marola; Olli Saari

doi:10.1007/s00013-015-0849-z

Homeomorphisms of the Heisenberg group preserving BMO

Riikka Korte, Niko Marola, Olli Saari

University of Helsinki

Research output: Contribution to journal › Article › Scientific › peer-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 language	English
Pages (from-to)	175-182
Number of pages	8
Journal	Archiv der Mathematik
Volume	106
Issue number	2
DOIs	https://doi.org/10.1007/s00013-015-0849-z
Publication status	Published - Feb 2016
MoE publication type	A1 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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10.1007/s00013-015-0849-z

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title = "Homeomorphisms of the Heisenberg group preserving BMO",

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.",

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

author = "Riikka Korte and Niko Marola and Olli Saari",

year = "2016",

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AU - Korte, Riikka

AU - Marola, Niko

AU - Saari, Olli

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N2 - 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.

AB - 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.

KW - Carnot group

KW - Function of bounded mean oscillation

KW - Heisenberg group

KW - Metric space

KW - Quasiconformal mapping

KW - Stratified group

KW - QUASI-CONFORMAL MAPPINGS

KW - MAPS

KW - QUASICONFORMALITY

KW - SPACES

U2 - 10.1007/s00013-015-0849-z

DO - 10.1007/s00013-015-0849-z

M3 - Article

SN - 0003-889X

VL - 106

SP - 175

EP - 182

JO - Archiv der Mathematik

JF - Archiv der Mathematik

IS - 2

ER -

Homeomorphisms of the Heisenberg group preserving BMO

Abstract

Keywords

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