Harmonic extensions of quasiregular maps
Pekka Pankka, Juan Souto

TL;DR
This paper proves that non-constant quasiregular selfmaps of the n-sphere can be extended harmonically into hyperbolic space, providing a new link between quasiregular maps and harmonic analysis.
Contribution
It establishes the existence of harmonic extensions for quasiregular maps on spheres into hyperbolic space, a novel result in geometric analysis.
Findings
Every non-constant quasiregular selfmap of the n-sphere admits a harmonic extension to hyperbolic space.
The extension exists for dimensions n ≥ 2.
The result bridges quasiregular maps and harmonic functions in geometric contexts.
Abstract
We prove that every non-constant quasiregular selfmap of the -sphere admits a harmonic extension to the hyperbolic space for .
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Analytic and geometric function theory · Geometric and Algebraic Topology
