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A big Picard theorem for quasiregular mappings into manifolds with many ends


Authors: Ilkka Holopainen and Pekka Pankka
Journal: Proc. Amer. Math. Soc. 133 (2005), 1143-1150
MSC (2000): Primary 30C65
DOI: https://doi.org/10.1090/S0002-9939-04-07599-9
Published electronically: October 14, 2004
MathSciNet review: 2117216
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Abstract | References | Similar Articles | Additional Information

Abstract: We study quasiregular mappings from a punctured Euclidean ball into $n$-manifolds with many ends and prove, by using Harnack's inequality, a version of the big Picard theorem.


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Additional Information

Ilkka Holopainen
Affiliation: Department of Mathematics, P.O. Box 4 (Yliopistonkatu 5), FIN-00014, University of Helsinki, Finland
Email: ilkka.holopainen@helsinki.fi

Pekka Pankka
Affiliation: Department of Mathematics, P.O. Box 4 (Yliopistonkatu 5), FIN-00014, University of Helsinki, Finland
Email: pekka.pankka@helsinki.fi

DOI: https://doi.org/10.1090/S0002-9939-04-07599-9
Keywords: Essential singularity, Harnack inequality, Picard theorem, quasiregular mappings
Received by editor(s): August 26, 2003
Received by editor(s) in revised form: December 2, 2003
Published electronically: October 14, 2004
Additional Notes: Both authors were supported in part by the Academy of Finland, project 53292.
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2004 American Mathematical Society