The Limiting Shape of One-dimensional Teichmüller Spaces

Infinite dimensional Teichmüller spaces

Remarks on the Hyperbolic Geometry of Product Teichmüller Spaces

Let e T be a cross product of n Teichmüller spaces of Fuchsian groups, n > 1. From the properties of Kobayashi metric and from the Royden-Gardiner theorem, e T is a complete hyperbolic manifold. Each two distinct points of e T can be joined by a hyperbolic geodesic segment, which is not in general unique. But when e T is finite dimensional or infinite dimensional of a certain kind, then among a...

Weil-Petersson Geometry of the Universal Teichmüller Space

The universal Teichmüller space T (1) is the simplest Teichmüller space that bridges spaces of univalent functions and general Teichmüller spaces. It was introduced by Bers [Ber65, Ber72, Ber73] and it is an infinite-dimensional complex Banach manifold. The universal Teichmüller space T (1) contains Teichmüller spaces of Riemann surfaces as complex submanifolds. The universal Teichmüller space ...

The Theory of Teichmüller Spaces – A View Towards Moduli Spaces of Kähler Manifolds

Universal Teichmüller Space

We present an outline of the theory of universal Teichmüller space, viewed as part of the theory of QS, the space of quasisymmetric homeomorphisms of a circle. Although elements of QS act in one dimension, most results about QS depend on a two-dimensional proof. QS has a manifold structure modelled on a Banach space, and after factorization by PSL(2,R) it becomes a complex manifold. In applicat...