Biharmonic Maps and Laguerre Minimal Surfaces

Yusuf Abu Muhanna and Rosihan M. Ali

Abstract and Applied Analysis, 2013, vol. 2013, 1-9

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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:843156

DOI: 10.1155/2013/843156

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