A Unified Approach to Univalence Criteria in the Unit Disc

Martin Chuaqui
1995 Proceedings of the American Mathematical Society  
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
more » ... part to a necessary one proved by Bergman and Schiffer.
doi:10.2307/2160900 fatcat:e76c5d5i3jg57koo4a4xhq6evi