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Biharmonic Maps and Laguerre Minimal Surfaces

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  • Yusuf Abu Muhanna
  • Rosihan M. Ali

Abstract

A Laguerre surface is known to be minimal if and only if its corresponding isotropic map is biharmonic. For every Laguerre surface is its associated surface , where lies in the unit disk. In this paper, the projection of the surface associated to a Laguerre minimal surface is shown to be biharmonic. A complete characterization of is obtained under the assumption that the corresponding isotropic map of the Laguerre minimal surface is harmonic. A sufficient and necessary condition is also derived for to be a graph. Estimates of the Gaussian curvature to the Laguerre minimal surface are obtained, and several illustrative examples are given.

Suggested Citation

  • Yusuf Abu Muhanna & Rosihan M. Ali, 2013. "Biharmonic Maps and Laguerre Minimal Surfaces," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, April.
    • Handle: RePEc:hin:jnlaaa:843156
    DOI: 10.1155/2013/843156
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