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

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Abstract

We identify nonparametric minimal surfaces \(\cal S\) 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 2π. This leads us to study periodic harmonic mappings defined on the left half-plane and univalent logharmonic mappings defined on the unit disk.

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Authors and Affiliations

  1. Department of Computer Science, Mathematics and Statistics, American University of Sharjah, Sharjah, U.A.E.

    Zayid Abdulhadi

  2. Department of Mathematics, Technion — Israel Institute of Technology, Haifa, 32000, Israel

    Daoud Bshouty

  3. Département de Mathématiques et de Statistique, Université Laval, Québec, G1K7P4, Canada

    Walter Hengartner

Authors
  1. Zayid Abdulhadi
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  2. Daoud Bshouty
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  3. Walter Hengartner
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Corresponding author

Correspondence to Zayid Abdulhadi.

Additional information

The second author’s work was supported in part by the Fund for the Promotion of Research at the Technion. The third author’s work was supported by grants from the NSERC of Canada and the FCAR of Quebec.

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Abdulhadi, Z., Bshouty, D. & Hengartner, W. Minimal Surfaces whose Gauss Map Covers Periodically the Pointed Upper Half-Sphere Exactly Once. Comput. Methods Funct. Theory 2, 155–174 (2003). https://doi.org/10.1007/BF03321014

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  • DOI: https://doi.org/10.1007/BF03321014

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