Abstract. For p ≥ 1, the p-integrable Teichmüller space is the metric subspace of the Teichmüller space composed of the Teichmüller equivalence classes with p-integrable Beltrami coefficient. In this paper, for p ≥ 2, we introduce a complex structure on the p-integrable Teichmüller space of an arbitrary Fuchsian group satisfying a certain geometric condition. As an application, we show the coincidence of two canonical distances on the metric subspace.

No abstract

No abstract

This paper deals with the smoothness and strongly pseudoconvexity of p-Weil-Petersson metric. This metric is a complex Finsler metric on the p-integrable Teichmüller space of a Riemann surface satisfying Lehner's condition, which is an extended concept of the Weil-Petersson metric on the square integrable Teichmüller space.

We first remark that the complex dilatation of a quasiconformal homeomorphism of a hyperbolic Riemann surface R obtained by the barycentric extension due to Douady-Earle vanishes at any cusp of R. Then we give a new proof, without using the Bers embedding, of a fact that the quasiconformal homeomorphism obtained by the barycentric extension from an integrable Beltrami coefficient on R is asymptotically conformal if R satisfies a certain geometric condition.