Journal d’Analyse Mathematique

, Volume 76, Issue 1, pp 337–347 | Cite as

A new proof of the Ahlfors five islands theorem



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.


Meromorphic Function Existence Theorem Periodic Point Quasiconformal Mapping Quasiregular Mapping 
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Copyright information

© Hebrew University of Jerusalem 1998

Authors and Affiliations

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

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