Definitions of quasiconformality

摘要

We establish that the infinitesimal "H"definition" for quusiconfor-nial mappings on Camel groups implies global qunsisymmctry.and hence the absolute continuity on almost all lines. Our method is new even in R" where we obtain that the "limsup" condition in the H-delinition can be replaced by a "liminf" condition. This leads "to u now removability result for (quasi)confonnul mappings in liiiclidctm spaces. Anapplication to parametrizations of chord-are surfaces is also given.