Holopainen, Ilkka; Rickman, Seppo A Picard type theorem for quasiregular mappings of \(\mathbb{R}^ n\) into \(n\)- manifolds with many ends. (English) Zbl 0763.30006 Rev. Mat. Iberoam. 8, No. 2, 131-148 (1992). 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. Reviewer: M.Vuorinen (Helsinki) Cited in 1 ReviewCited in 7 Documents MSC: 30C65 Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations Keywords:quasiregular maps; Picard theorem PDF BibTeX XML Cite \textit{I. Holopainen} and \textit{S. Rickman}, Rev. Mat. Iberoam. 8, No. 2, 131--148 (1992; Zbl 0763.30006) Full Text: DOI EuDML OpenURL