THE DISTANCE BETWEEN DIFFERENT COMPONENTS OF THE UNIVERSAL TEICHMULLER SPACE

The model of the universal Teichmuller union of infinite disconnected components. between different components is 0, and the every other component is 2. space by the derivatives of logarithm is the In this paper, it is proved that the distance distance from the center of a component to

Some Remarks on the Geodesics in Infinite Dimensional Teichmuller Spaces

Let B denote the set of those points p in an infinite dimensional Teichmiiller space such that a geodesic between the zero point and p is not unique. Some properties of the set B are given.

Besov Functions and Tangent Space to the Integrable Teichmüller Space

The authors identify the function space which is the tangent space to the integrable Teichmfiller space. By means of quasiconformal deformation and an operator induced by a Zygmund function, several characterizations of this function space are obtained.

On Nonuniqueness of Geodesics and Geodesic Disks in the Universal Asymptotic Teichmüller Space

Abstract The non-uniqueness on geodesics and geodesic disks in the universal asymptotic Teichmfiller space AT（D） are studied in this paper. It is proved that if # is asymptotically extremal in [[#]] with h （μ） 〈 h＊ （μ） for some point ζ∈D, then there exist infinitely many geodesic segments joining [[0]] and [[μ]], and infinitely many holomorphic geodesic disks containing [[0]] and [μ]] in AT（D）.

Isomorphisms of fiber spaces over Teichmüller spaces

We will be mainly concerned with some important fiber spaces over Teichmuller spaces, including the Bers fiber space and Teichmuller curve, establishing an isomorphism theorem between 'punctured' Teichmuller curves and determining the biholomorphic isomorphisms of these fiber spaces.

Some characterizations of the integrable Teichmller space

In this paper, we prove that the Bers projection of the integrable Teichmller space is holomorphic. By using the Douady-Earle extension, we obtain some characterizations of the integrable Teichmller space as well as the p-integrable asymptotic affine homeomorphism.

On Holomorphic Sections in Teichmiiller Spaces

It is proved that, for any elementary torsion free Fuchsian group F, the natural projection from the Teichmiiller curve V（F） to the Teichmiiller space T（F） has no holomorphic section.

Inequalities on the Inner Radius of Univalency and the Norm of Pre-Schwarzian Derivative

In this paper, we get a lower bound of inner radius of univalency of Schwarzian derivative by means of the norm of pre-Schwarzian derivative. Furthermore, we apply the theory of Universal Teichmuller Space to explain its geometric meaning which shows the relationship between the inner radius in Universal Teichmuller Space embedded by Schwarzian derivative and the norm defined in Universal Teichmuller Space embedded by pre-Schwarzian derivative.

On the inner radius of univalency by pre-Schwarzian derivative

In this paper,the inner radius of univalency of hyperbolic domains by pre-Schwarzian derivative is studied,and some general formulas for the lower bound of the inner radius are established. As their applications,the lower bounds of inner radiuses for angular domains and strongly starlike domains are obtained.

An isomorphism theorem for Teichmüller curves

It is proved that for any Fuchsian group Г such that H/Г is a hyperbolic Riemann surface, the Teichmuller curve V(Г) has a unique complex manifold structure so that the natural projection of the Bers fiber space F(Г) onto V(Г) is holomorphic with local holomorphic sections. An isomorphism theorem for Teichmuller curves is deduced, which generalizes a classical result that the Teichmuller curve V(Г) depends only on the type of Г and not on the orders of the elliptic elements of Г when H/Г is a compact hyperbolic Riemann surface.