In this article we characterize the univalent harmonic mappings from the exterior of the unit disk, $Delta$, onto a simply connecteddomain $Omega$ containing infinity and which are solutions of the systemof elliptic partial differential equations $fzbb = a(z)f_z(z)$where the second dilatation function $a(z)$ is a finite Blaschkeproduct. At the end of this article, we apply our results tononparametric minimal surfaces having the property that the imageof its Gauss map is the upper half-sphere covered once or twice.
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