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2013 Biharmonic Maps and Laguerre Minimal Surfaces
Yusuf Abu Muhanna, Rosihan M. Ali
Abstr. Appl. Anal. 2013: 1-9 (2013). DOI: 10.1155/2013/843156


A Laguerre surface is known to be minimal if and only if its corresponding isotropic map is biharmonic. For every Laguerre surface Φ is its associated surface Ψ = 1 + u 2 Φ , where u lies in the unit disk. In this paper, the projection of the surface Ψ associated to a Laguerre minimal surface is shown to be biharmonic. A complete characterization of Ψ 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 Ψ to be a graph. Estimates of the Gaussian curvature to the Laguerre minimal surface are obtained, and several illustrative examples are given.


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Yusuf Abu Muhanna. Rosihan M. Ali. "Biharmonic Maps and Laguerre Minimal Surfaces." Abstr. Appl. Anal. 2013 1 - 9, 2013.


Published: 2013
First available in Project Euclid: 27 February 2014

zbMATH: 1275.53013
MathSciNet: MR3045000
Digital Object Identifier: 10.1155/2013/843156

Rights: Copyright © 2013 Hindawi

Vol.2013 • 2013
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