Definitions of quasiconformality

Summary We establish that the infinitesimal H-definition for quasiconformal mappings on Carnot groups implies global quasisymmetry, and hence the absolute continuity on almost all lines. Our method is new even inR ⁿ where we obtain that the limsup condition in theH-definition can be replaced by a liminf condition. This leads to a new removability result for (quasi)conformal mappings in Euclidean spaces. An application to parametrizations of chord-arc surfaces is also given.Oblatum 25-IV-1994 & 9-VI-1994Both authors supported in part by NSF. The first author also acknowledges the support of the Academy of Finland and the Sloan Foundation.