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.
"Biharmonic Maps and Laguerre Minimal Surfaces." Abstr. Appl. Anal. 2013 1 - 9, 2013. https://doi.org/10.1155/2013/843156