Invariant operators and univalent functions

Harmelin, Reuven

doi:10.1090/S0002-9947-1982-0662063-1

Invariant operators and univalent functions
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Trans. Amer. Math. Soc. 272 (1982), 721-731 Request permission

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 $\ge 3$, 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.

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Über den Zusammengang einiger Charakteristiken eines einfach zusammenhängenden Bereiches mit der Kreis abbildung

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