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Rescaling principle for isolated essential singularities of quasiregular mappings

2012

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.

Unit sphereEssential singularityClass (set theory)Pure mathematicsmath.CVMathematics - Complex VariablesMathematics::Complex VariablesEuclidean spacemath.MGApplied MathematicsGeneral MathematicsPrimary 30C65 Secondary 53C21 32H02010102 general mathematics16. Peace & justiceMathematics::Geometric Topology01 natural sciencesRescaling010101 applied mathematicsQuasiregular mappingMathematics - Metric GeometryIsolated essential singularities111 MathematicsGravitational singularity0101 mathematicsMathematicsProceedings of the American Mathematical Society
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