A generalization of the Picard theorem

Abstract

We recall the notions of conformal and quasiconformal mappings \textit{in the sense of Gromov}, extending the classical notions of conformal and quasiconformal mappings, and prove the following theorem. {\em If the mapping $F:{\mathbb{R}}^n\to {\mathbb{R}}^2$, where $n\ge 2$, quasiconformal in the sense of Gromov, omits more than one value on the plane ${\mathbb{R}}^2$, then it is a constant mapping.}

References in corpus (2)

• Value distribution and potential theory
• Conformality in the sense of Gromov and a generalized Liouville theorem