Integrably asymptotic affine homeomorphisms of the circle and Teichmüller spaces

摘要

A quasisymmetric homeomorphism of the unit circle S1 is called integrably asymptotic affine if it admits a quasiconformal extension into the unit disk so that its complex dilatation is square in-tegrable in the Poincare metric on the unit disk. Let QS* ( S1) be the space of such maps. Here we give some characterizations and properties of maps in QS* (S1). We also show that QS, (S1)/Moo (S1) is the completion of Diff( S1)/M6b( S1) in the Weil-Petersson metric.