TL;DR
This paper establishes a fundamental relationship between the distortion functions of harmonic surfaces and their Gauss maps, showing they are equivalent in quasiregularity under certain conditions, which deepens understanding of harmonic surface geometry.
Contribution
It proves that the distortion function of the Gauss map of a harmonic surface matches that of the surface itself, linking their quasiregularity properties.
Findings
Gauss map distortion equals surface distortion for harmonic surfaces
Gauss map is quasiregular iff the surface is quasiregular (non-planar case)
Results apply to regular Gauss maps of harmonic surfaces
Abstract
We prove that the distortion function of the Gauss map of a harmonic surface coincides with the distortion function of the surface. Consequently, Gauss map of a harmonic surface is quasiregular if and only if the surface is quasiregular, provided that the Gauss map is regular or what is shown to be the same, provided that the surface is non-planar.
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