The Differential of a Quasi-conformal Mapping of a Carnot-Caratheodry Space.
Quasihomography is a useful notion to represent a sense-preserving automorphism of the unit circle T which admits a quasiconformal extension to the unit disc. For K ≥ 1 let denote the family of all K-quasihomographies of T. With any we associate the Douady-Earle extension and give an explicit and asymptotically sharp estimate of the norm of the complex dilatation of .