Kobayashi’s and Teichmüller’s Metrics on the Teichmüller Space of Symmetric Circle Homeomorphisms

Characterization of the Asymptotic Teichmüller Space of the Open Unit Disk through Shears

We give a parametrization of the asymptotic Teichmüller space AT (D) of the open unit disk through a space of equivalent classes of the shear functions induced by quasisymmetric homeomorphisms on the Farey tesselation of the disk. Then using the parametrization, we define a metric on AT (D). Two other related metrics are also introduced on AT (D) by using cross-ratio distortions or quadrilatera...

Quasiconformal Homeomorphisms and Dynamics III: The Teichmüller space of a holomorphic dynamical system

Weil-petersson Metric on the Universal Teichmüller Space Ii. Kähler Potential and Period Mapping

We study the Hilbert manifold structure on T0(1) — the connected component of the identity of the Hilbert manifold T (1). We characterize points on T0(1) in terms of Bers and pre-Bers embeddings, and prove that the Grunsky operators B1 and B4, associated with the points in T0(1) via conformal welding, are Hilbert-Schmidt. We define a “universal Liouville action” — a real-valued function S1 on T...

Function Models for Teichmüller Spaces and Dual Geometric Gibbs Type Measure Theory for Circle Dynamics

Geometric models and Teichmüller structures have been introduced for the space of smooth circle endomorphisms and for the space of uniformly symmetric circle endomorphisms. The latter one is the completion of the previous one under the Techmüller metric. Moreover, the spaces of geometric models as well as the Teichmüller spaces can be described as the space of Hölder continuous scaling function...

Teichmüller Theory and the Universal Period Mapping via Quantum Calculus and the H Space on the Circle

Quasisymmetric homeomorphisms of the circle, that arise in the Teichmüller theory of Riemann surfaces as boundary values of quasiconfomal diffeomorphisms of the disk, have fractal graphs in general and are consequently not so amenable to usual analytical or calculus procedures. In this paper we make use of the remarkable fact this group QS(S) acts by substitution (i.e., pre-composition) as a fa...