Sharpness of Rickman's Picard theorem in all dimensions

Abstract

We show that given $n\ge 3$, $q\ge 1$, and a finite set $\{y_1,\dots ,y_q\}$ in ${\mathbb{R}}^n$ there exists a quasiregular mapping ${\mathbb{R}}^n\to {\mathbb{R}}^n$ omitting exactly points $y_1,\dots ,y_q$.

74 pages, 55 figures

Cited by in corpus (1)

• Quasiregular mappings on sub-Riemannian manifolds