Integrably asymptotic affine homeomorphisms of the circle and Teichmüller spaces (Q1585587)

A quasisymmetric homeomorphism of the unit circle \(S'\) is said to be integrably asymptotic affine if it admits a quasiconformal extension into the unit disk such that its complex dilatation is square integrable with the Poincaré metric on the unit disc. Let \(QS_*(S')\) be the space of such quasisymmetric homeomorphisms of \(S\)! In this paper, some characterizations of maps in \(QS_*(S')\) are given. The Weil-Petersson metric is introduced to \(QS_*(S')/ \text{Möb}(S')\) and it is shown that this metric is complete.