A generalization of the Picard theorem

2021/08/11 by Владимир Антонович Зорич, Zorich, V. A.
Mathematics · #Analytic and geometric function theory #Geometric Analysis and Curvature Flows #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2108.05161

Abstract

We recall the notions of conformal and quasiconformal mappings in the sense of Gromov, extending the classical notions of conformal and quasiconformal mappings, and prove the following theorem. \em If the mapping F: ℝⁿ → ℝ² , where n ≥ 2 , quasiconformal in the sense of Gromov, omits more than one value on the plane ℝ² , then it is a constant mapping.

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