Ruscheweyh's univalence criterion and quasiconformal extensions

Univalence criteria for meromorphic functions and quasiconformal extensions

The aim of this paper is to obtain sufficient conditions for univalence of meromorphic functions in the U *. Also, we refine a quasiconformal extension criterion with the help of Becker's method. A number of univalence conditions would follow upon specializing the parameters involved in our main results. 1 Introduction We denote by U r = {z ∈ C : |z| < r} ( < r ≤ ) the disc of radius r and le...

Univalence Criterion for Analytic Functions

In this paper, we obtain a new univalence criterion for analytic functions defined outside of the unit disk. Relevant connections of the results, which are presented in this paper with various known results are also considered. 2000 Mathematics Subject Classification: Primary 30C45.

General Univalence Criteria in the Disk: Extensions and Extremal Function

Many classical univalence criteria depending on the Schwarzian derivative are special cases of a result, proved in [18], involving both conformal mappings and conformal metrics. The classical theorems for analytic functions on the disk emerge by choosing appropriate conformal metrics and computing a generalized Schwarzian. The results in this paper address questions of extending functions which...

Some Remarks Concerning Quasiconformal Extensions in Several Complex Variables

Evolution Dynamics of Conformal Maps with Quasiconformal Extensions

We study one-parameter curves on the universal Teichmüller space T and on the homogeneous space M = Diff S/Rot S embedded into T . As a result, we deduce evolution equations for conformal maps that admit quasiconformal extensions and, in particular, such that the associated quasidisks are bounded by smooth Jordan curves. Some applications to Hele-Shaw flows of viscous fluids are given.