On generalized quasiregular mappings

Abstract

We study classes of continuous, open, discrete mappings satisfying some modular inequalities and show that these inequalities ensure important geometric properties, extending partially known results from the theory of quasiregular mappings, such as Liouville, Picard, Montel theorems and equicontinuity results. Most of the theorems are obtained in dimension n ≥ 2.

Keywords:

• Sobolev mappings satisfying generalized modular inequalities
• generalizations of quasiregular mappings
• geometric properties of Sobolev mappings

AMS Subject Classification:

• 30C65

Acknowledgements

We thank the referee for his comments.