Article ID Journal Published Year Pages File Type
4673100 Indagationes Mathematicae 2013 13 Pages PDF
Abstract
We prove that the distortion function of the Gauss map of a surface parametrized by harmonic coordinates coincides with the distortion function of the parametrization. Consequently, the Gauss map of a harmonic surface is K quasiconformal if and only if its harmonic parametrization is K quasiconformal, provided that the Gauss map is regular or what is shown to be the same, provided that the surface is non-planar. This generalizes the classical result that the Gauss map of a minimal surface is a conformal mapping.
Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
Authors
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