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A Picard type theorem for quasiregular mappings of \(\mathbb{R}^ n\) into \(n\)- manifolds with many ends. (English) Zbl 0763.30006

The second author proved a generalization of Picard’s theorem for quasiregular maps of Euclidean spaces in 1980. Here a generalization of this earlier result is given to the case when the target is no longer an Euclidean space but an \(n\)-manifold. Some of the ideas used in the proofs rely on recent work of A. Eremenko and J. Lewis. In particular, the authors use the measure \(\mu\) associated to an \(A\)-harmonic function given by the Riesz representation theorem.

MSC:

30C65 Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations
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