DEFINITIONS OF QUASICONFORMALITY

We establish that the infinitesimal ''H-definition'' for quasiconforma l mappings on Carnot groups implies global quasisymmetry, and hence th e absolute continuity on almost all lines. Our method is new even in R (n) where we obtain that the ''limsup'' condition in the H-definition can be replaced by a ''liminf'' condition. This leads to a new removab ility result for (quasi)conformal mappings in Euclidean spaces. An app lication to parametrizations of chord-are surfaces is also given.