Invariant operators and univalent functions-Reference-Cited by-同舟云学术

Invariant operators and univalent functions

Published:1982 Issue:2 Volume:272 Page:721-731
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Harmelin Reuven

Abstract

Necessary and sufficient conditions for univalence of meromorphic functions in certain domains in the complex plane are established in terms of some differential operators of degrees ≥ 3 \ge 3 , possessing the same invariance property as the Schwarzian derivative. Those operators include the derivatives of the Schwarzian derivative and Aharonov’s invariants. Conditions for the existence of quasiconformal extensions are also achieved.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1982-272-02/S0002-9947-1982-0662063-1/S0002-9947-1982-0662063-1.pdf

Reference14 articles.

1. A necessary and sufficient condition for univalence of a meromorphic function;Aharonov, Dov;Duke Math. J.,1969

2. Quasiconformal reflections;Ahlfors, Lars V.;Acta Math.,1963

3. Riemann’s mapping theorem for variable metrics;Ahlfors, Lars;Ann. of Math. (2),1960

4. A uniqueness theorem for Beltrami equations;Ahlfors, L.;Proc. Amer. Math. Soc.,1962

5. Schwarzian derivatives, the Poincaré metric and the kernel function;Beardon, A. F.;Comment. Math. Helv.,1980

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