Journal d’Analyse Mathematique

, Volume 76, Issue 1, pp 337–347

A new proof of the Ahlfors five islands theorem


DOI: 10.1007/BF02786941

Cite this article as:
Bergweiler, W. J. Anal. Math. (1998) 76: 337. doi:10.1007/BF02786941


We deduce the Ahlfors five islands theorem from a corresponding result of Nevanlinna concerning perfectly branched values, a rescaling lemma for non-normal families and an existence theorem for quasiconformal mappings. We also give a proof of Nevanlinna’s result based on the rescaling lemma and a version of Schwarz’s lemma.

Copyright information

© Hebrew University of Jerusalem 1998

Authors and Affiliations

  1. 1.Mathematisches SeminarChristian-Albrechts-UniversitÄt zu KielKielGermany