## 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

### Keywords:

quasiregular maps; Picard theorem
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