Sharpness of Rickman's Picard theorem in all dimensions

2013/04/25 by Drasin, David, Pankka, Pekka · 1 citation
#30C65 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1304.6998

Abstract

We show that given n≥ 3, q≥ 1, and a finite set \y₁,…, y_q\ in \mathbb Rⁿ there exists a quasiregular mapping \mathbb Rⁿ → \mathbb Rⁿ omitting exactly points y₁,…, y_q.

Cited by

• The Heinonen-Semmes problems after thirty years

Related

• The Rickman-Picard Theorem
• A generalization of the Picard theorem
• Nonremovable sets for Hölder continuous quasiregular mappings in the plane
• Wiman and Arima theorems for quasiregular mappings
• Quasiregular cobordism theorem