Picard's Theorem and Rickman's Theorem by Way of Harnack's Inequality

DOI10.2307/2160861zbMath0807.30010OpenAlexW4255285235MaRDI QIDQ4311391

John L. Lewis

Publication date: 2 March 1995

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2160861

zbMATH Keywords

quasiregular mappingharmonic functionsHarnack's inequalityPicard's theorem

Mathematics Subject Classification ID

Quasiconformal mappings in (mathbb{R}^n), other generalizations (30C65) Entire functions of one complex variable (general theory) (30D20)

Related Items (13)

A big Picard theorem for quasiregular mappings into manifolds with many ends ⋮ Estimates on derivatives and logarithmic derivatives of holomorphic functions and Picard's theorem ⋮ Quasiregular maps on Carnot groups ⋮ On the range of harmonic maps in the plane ⋮ Sharpness of Rrickman's Picard theorem in all dimensions ⋮ On Picard's theorem ⋮ Picard's theorem and the Rickman construction ⋮ Arakelyan's theorem and relations between two harmonic functions ⋮ An extension of Lewis's Lemma, renormalization of harmonic and analytic functions, and normal families ⋮ Estimates on partial derivatives and logarithmic partial derivatives of holomorphic functions on polydiscs and beyond ⋮ 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

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