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Exterior Univalent Harmonic Mappings With Finite Blaschke Dilatations

  Published:1999-06-01
 Printed: Jun 1999
  • D. Bshouty
  • W. Hengartner
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Abstract

In this article we characterize the univalent harmonic mappings from the exterior of the unit disk, $\Delta$, onto a simply connected domain $\Omega$ containing infinity and which are solutions of the system of elliptic partial differential equations $\fzbb = a(z)f_z(z)$ where the second dilatation function $a(z)$ is a finite Blaschke product. At the end of this article, we apply our results to nonparametric minimal surfaces having the property that the image of its Gauss map is the upper half-sphere covered once or twice.
Keywords: harmonic mappings, minimal surfaces harmonic mappings, minimal surfaces
MSC Classifications: 30C55, 30C62, 49Q05 show english descriptions General theory of univalent and multivalent functions
Quasiconformal mappings in the plane
Minimal surfaces [See also 53A10, 58E12]
30C55 - General theory of univalent and multivalent functions
30C62 - Quasiconformal mappings in the plane
49Q05 - Minimal surfaces [See also 53A10, 58E12]
 

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