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Rescaling principle for isolated essential singularities of quasiregular mappings

Authors: Yûsuke Okuyama and Pekka Pankka
Journal: Proc. Amer. Math. Soc. 143 (2015), 2043-2050
MSC (2010): Primary 30C65; Secondary 53C21, 32H02
Published electronically: December 3, 2014
MathSciNet review: 3314113
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Abstract: We establish a rescaling theorem for isolated essential singularities of quasiregular mappings. As a consequence we show that the class of closed manifolds receiving a quasiregular mapping from a punctured unit ball with an essential singularity at the origin is exactly the class of closed quasiregularly elliptic manifolds, that is, closed manifolds receiving a non-constant quasiregular mapping from a Euclidean space.

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Additional Information

Yûsuke Okuyama
Affiliation: Division of Mathematics, Kyoto Institute of Technology, Sakyo-ku, Kyoto 606-8585, Japan

Pekka Pankka
Affiliation: Department of Mathematics and Statistics (P.O. Box 68), University of Helsinki, FI-00014 University of Helsinki, Finland – and – Department of Mathematics and Statistics (P.O. Box 35), FI-40014 University of Jyväskylä, Jyväskylä, Finland

Keywords: Rescaling, isolated essential singularities, quasiregular mapping
Received by editor(s): January 13, 2013
Received by editor(s) in revised form: October 1, 2013
Published electronically: December 3, 2014
Additional Notes: The first author was partially supported by JSPS Grant-in-Aid for Young Scientists (B), 24740087.
The second author was partially supported by the Academy of Finland project #256228.
Communicated by: Jeremy Tyson
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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