A univalency criterion
type: Item
instance of: scholarly article
title: A univalency criterion
zbMATH Open document ID: 0574.30023
author: J. Milne Anderson
author: Aimo Hinkkanen
published in: Michigan Mathematical Journal
publication date: 1985-01-01T00:00:00Z
review text: Let f be meromorphic and locally univalent in the upper half plane U with Schwarzian derivative S(f,z). Suppose that \(| 2(Im z)S(f,z)-c(c- 1)| \leq k| c|\) for all \(z\in U\). It is shown that if \(| c-1| \leq k<1,\) then f is univalent and has a k-quasiconformal extension to the Riemann sphere, and that if \(| c-1| <1\) and \(k=1\), then f is univalent. This was conjectured by \textit{L. V. Ahlfors} in Discontin. Groups Riemann Surf., Proc. 1973 Conf. Univ. Maryland, 23- 29 (1974; Zbl 0324.30034).
Mathematics Subject Classification ID: 30C62
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 3916662
zbMATH Keywords: Schwarzian derivative
zbMATH Keywords: quasiconformal extension
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029003129
OpenAlex ID: W1976361572
DOI: 10.1307/MMJ/1029003129
description: scientific article; zbMATH DE number 3916662