Global contact and quasiconformal mappings of Carnot groups
Michael G. Cowling, Alessandro Ottazzi
TL;DR
This paper investigates the properties of quasiconformal and contact mappings on rigid Carnot groups, revealing that quasiconformal mappings are affine while contact mappings are not necessarily quasiconformal or affine.
Contribution
It establishes that globally defined quasiconformal mappings on rigid Carnot groups are affine, contrasting with contact mappings which may lack quasiconformality.
Findings
Quasiconformal mappings of rigid Carnot groups are affine.
Contact mappings of rigid Carnot groups are not necessarily quasiconformal.
Not all contact mappings are affine or quasiconformal.
Abstract
We show that globally defined quasiconformal mappings of rigid Carnot groups are affine, but that globally defined contact mappings of rigid Carnot groups need not be quasiconformal, and a fortiori not affine.
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