Criteria for univalence and quasiconformal extension of harmonic mappings in terms of the Schwarzian derivative
نویسندگان
چکیده
منابع مشابه
The Schwarzian Derivative for Harmonic Mappings
The Schwarzian derivative of an analytic function is a basic tool in complex analysis. It appeared as early as 1873, when H. A. Schwarz sought to generalize the Schwarz-Christoffel formula to conformal mappings of polygons bounded by circular arcs. More recently, Nehari [5, 6, 7] and others have developed important criteria for global univalence in terms of the Schwarzian derivative, exploiting...
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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...
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ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 2014
ISSN: 0003-889X,1420-8938
DOI: 10.1007/s00013-014-0714-5