The analogue of Picard's theorem for quasiregular mappings in dimension three

DOI10.1007/BF02392472zbMath0617.30024MaRDI QIDQ1821902

Seppo Rickman

Publication date: 1985

Published in: Acta Mathematica (Search for Journal in Brave)

zbMATH Keywords

value distributionquasiregular mapping

Mathematics Subject Classification ID

Quasiconformal mappings in the complex plane (30C62)

Related Items (29)

Remarks on the local index of quasiregular mappings ⋮ Proof of a conjecture of F. Nevanlinna concerning functions which have deficiency sum two ⋮ On the Teichmüller-Wittich-Belinskij theorem ⋮ On value distributions for quasimeromorphic mappings on \(\mathbb H\)-type Carnot groups ⋮ Permutable quasiregular maps ⋮ Quasiregular maps on Carnot groups ⋮ Iteration of quasiregular mappings ⋮ Quasiregularly elliptic link complements ⋮ The fast escaping set for quasiregular mappings ⋮ Foundations for an iteration theory of entire quasiregular maps ⋮ Bloch's theorem for mappings of bounded and finite distortion ⋮ Sharpness of Rrickman's Picard theorem in all dimensions ⋮ Quasiregular mappings of the Heisenberg group ⋮ Fatou–Julia theory for non-uniformly quasiregular maps ⋮ Unnamed Item ⋮ Picard's theorem and the Rickman construction ⋮ A note on asymptotic values of quasiregular maps ⋮ Extending rational maps ⋮ Quasiregular mappings and cohomology. ⋮ The escaping set of a quasiregular mapping ⋮ On the iteration of quasimeromorphic mappings ⋮ Quasiregular mappings in even dimensions ⋮ Classification of Riemannian manifolds in nonlinear potential theory ⋮ On slow escaping and non-escaping points of quasimeromorphic mappings ⋮ New proofs of Liouville's theorem and little Picard's theorem for harmonic functions on \(R^n \), \(n\ge 2\) ⋮ The Rickman–Picard theorem ⋮ A bound on the cohomology of quasiregularly elliptic manifolds ⋮ Mappings of finite distortion: the Rickman-Picard theorem for mappings of finite lower order ⋮ Geometric branched covers between generalized manifolds

Cites Work

• Quasiregular mappings and metrics on the n-sphere with punctures
• Averages of the counting function of a quasiregular mapping
• On the number of omitted values of entire quasiregular mappings
• A defect relation for quasimeromorphic mappings
• Deformation classes of meromorphic functions and their extensions to interior transformations
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