A generalization o f Nehari ' s univalence criterion BRAD OSGOOD AND DENNIS STOWE

This note is a sequel to our paper [OS] where we generalized the Schwarzian derivative to conformal mappings of Riemannian manifolds. There we found that many of the phenomena familiar from the classical theory have counterparts in the more general setting. Here we advance this another step by giving a generalization of the well known univalence criterion of Nehari [N]. Despite its relatively advanced age, this result continues to generate interest, see [L]. The argument used here in the general case, if specialized to the situation considered by Nehari, gives a somewhat different and a more geometric proof of his theorem than is often presented. We want to keep this note short, since the proof of the Theorem is really quite simple, and also fairly self-contained. We shall need a number of facts from our earlier paper and we collect them here with very little additional discussion. We refer the reader to that paper for more details.