Geodesic
Exterior Univalent Harmonic Mappings With Finite Blaschke Dilatations
Canadian journal of mathematics, Tome 51 (1999) no. 3, pp. 470-487

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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 $\overline{{{f}_{{\bar{z}}}}\left( Z \right)}=a\left( z \right){{f}_{z}}\left( z \right)$ where the second dilatation function $a\left( z \right)$ 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.
DOI : 10.4153/CJM-1999-021-8
Mots-clés : 30C55, 30C62, 49Q05, harmonic mappings, minimal surfaces 
Bshouty, D.; Hengartner, W. Exterior Univalent Harmonic Mappings With Finite Blaschke Dilatations. Canadian journal of mathematics, Tome 51 (1999) no. 3, pp. 470-487. doi: 10.4153/CJM-1999-021-8
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