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A unified approach to univalence criteria in the unit disc

Author: Martin Chuaqui
Journal: Proc. Amer. Math. Soc. 123 (1995), 441-453
MSC: Primary 30C35; Secondary 30C62
MathSciNet review: 1233965
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Abstract: From the recent injectivity criterion of Osgood and Stowe we recover many of the known univalence criteria in the unit disc D and derive as well new conditions on D and simply-connected domains. While the criteria of Epstein can be established in this fashion, we show how the 'diameter term' in the criterion of Osgood and Stowe gives a sharper form of a condition of Ahlfors. Finally, on simply-connected domains we find a sufficient condition for univalence that is the counterpart to a necessary one proved by Bergman and Schiffer.

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