Weil–Petersson Teichmüller space III: dependence of Riemann mappings for Weil–Petersson curves

Function Model of the Teichmüller Space of a Closed Hyperbolic Riemann Surface

We introduce a function model for the Teichmüller space of a closed hyperbolic Riemann surface. Then we introduce a new metric by using the maximum norm on the function space on the Teichmüller space. We prove that the identity map from the Teichmüller space equipped with the usual Teichmüller metric to the Teichmüller space equipped with this new metric is uniformly continuous. Furthermore, we...

Canonical Mappings between Teichmüller Spaces

Introduction. In an important survey article [BIO] Bers reported on the state of knowledge of Teichmüller theory. There has been a lot of progress in the field since that time. The purpose of this paper is to summarize the recent work in one area of Teichmüller space theory. We will concentrate on the hyperbolic properties of Teichmüller spaces, and present as many consequences of this hyperbol...

Growth of the Weil-petersson Inradius of Moduli Space

In this paper we study the systole function along WeilPetersson geodesics. We show that the square root of the systole function is uniform Lipschitz on the Teichmüller space endowed with the Weil-Petersson metric. The inradius of a metric space is the largest radius of metric balls contained in the interior of the metric space. As applications of the result above, we study the growth of the Wei...

Quantum Teichmüller Space

We describe explicitly a noncommutative deformation of the *-algebra of functions on the Teichmüller space of Riemann surfaces with holes equivariant w.r.t. the mapping class group action.

Dynamics over Teichmüller Space