Rescaling principle for isolated essential singularities of quasiregular mappings

TL;DR

This paper proves a rescaling theorem for isolated essential singularities in quasiregular mappings and characterizes the class of closed manifolds that admit such mappings from punctured Euclidean spaces.

Contribution

It introduces a rescaling principle for essential singularities and characterizes manifolds that can be mapped quasiregularly from punctured Euclidean spaces.

Findings

Rescaling theorem for isolated essential singularities.

Characterization of closed manifolds with quasiregular mappings from punctured spaces.

Identification of quasiregularly elliptic manifolds.

Abstract

We establish a rescaling theorem for isolated essential singularities of quasiregular mappings. As a consequence we show that the class of closed manifolds receiving a quasiregular mapping from a punctured unit ball with an essential singularity at the origin is exactly the class of closed quasiregularly elliptic manifolds, that is, closed manifolds receiving a non-constant quasiregular mapping from a Euclidean space.