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

Holopainen, Ilkka; Rickman, Seppo

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)

MSC:

30C65

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

Keywords:

quasiregular maps; Picard theorem