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Computational Methods and Function Theory 2 (2002), No. 1, 155--174
Copyright Heldermann Verlag 2002

Minimal Surfaces whose Gauss Map Covers Periodically the Pointed Upper Half-Sphere Exactly Once

Zayid Abdulhadi
zahadi@hotmail.com, Department of Computer Science, Mathematics and Statistics, American University of Sharjah, Sharjah, U.A.E.

Daoud Bshouty
daoud@techunix.technion.ac.il, Department of Mathematics, Technion --- Israel Institute of Technology, Haifa 32000, Israel.

Walter Hengartner
walheng@mat.ulaval.ca, Département de Mathématiques et de Statistique, Université Laval, Québec G1K7P4, Canada.

[Abstract-pdf] [Abstract-ps]
We identify nonparametric minimal surfaces $S$ which have the property that their Gauss map $\vec{n}$ is periodic and covers the upper half-sphere minus the point $(0,0,1)$ exactly once on each horizontal half-strip of height~$2\pi$. This leads us to study periodic harmonic mappings defined on the left half-plane and univalent logharmonic mappings defined on the unit disk.

Keywords: Harmonic mappings, minimal surfaces.

MSC 2000: Primary 30C55; Secondary 30C62, 49Q05.

[FullText-pdf (256 K)] [FullText-ps (352 K)]