Teichmüller spaces and holomorphic dynamics

Liftings of Holomorphic Maps into Teichmüller Spaces

We study liftings of holomorphic maps into some Teichmüller spaces. We also study the relationship between universal holomorphic motions and holomorphic lifts into Teichmüller spaces of closed sets in the Riemann sphere.

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

A special subspace of weighted spaces of holomorphic functions on the upper half plane

In this paper, we intend to define and study concepts of weight and weighted spaces of holomorphic (analytic) functions on the upper half plane. We study two special classes of these spaces of holomorphic functions on the upper half plane. Firstly, we prove these spaces of holomorphic functions on the upper half plane endowed with weighted norm supremum are Banach spaces. Then, we investigate t...

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...

A remark on boundedness of composition operators between weighted spaces of holomorphic functions on the upper half-plane

In this paper, we obtain a sucient condition for boundedness of composition operators betweenweighted spaces of holomorphic functions on the upper half-plane whenever our weights are standardanalytic weights, but they don't necessarily satisfy any growth condition.