Sharpness of Rickman’s Picard theorem in all dimensions

David Drasin Department of Mathematics, Purdue University Pekka Pankka Department of Mathematics and Statistics, P.O. Box 68, (Gustaf Hällströmin katu 2b), University of Helsinki, Finland

Dynamical Systems mathscidoc:1701.11008

Acta Mathematica, 214, (2), 209-306, 2013.4
We show that given $${n \geqslant 3}$$ , $${q \geqslant 1}$$ , and a finite set $${\{y_1, \ldots, y_q \}}$$ in $${\mathbb{R}^n}$$ there exists a quasiregular mapping $${\mathbb{R}^n\to \mathbb{R}^n}$$ omitting exactly points $${y_1, \ldots, y_q}$$ .
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  title={Sharpness of Rickman’s Picard theorem in all dimensions},
  author={David Drasin, and Pekka Pankka},
  booktitle={Acta Mathematica},
David Drasin, and Pekka Pankka. Sharpness of Rickman’s Picard theorem in all dimensions. 2013. Vol. 214. In Acta Mathematica. pp.209-306.
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