Bi-quartic parametric polynomial minimal surfaces Available to Purchase

Minimal surfaces with isothermal parameters admitting Bézier representation were studied by Cosín and Monterde. They showed that, up to an affine transformation, the Enneper surface is the only bi-cubic isothermal minimal surface. Here we study bi-quartic isothermal minimal surfaces and establish the general form of their generating functions in the Weierstrass representation formula. We apply an approach proposed by Ganchev to compute the normal curvature and show that, in contrast to the bi-cubic case, there is a variety of bi-quartic isothermal minimal surfaces. Based on the Bézier representation we establish some geometric properties of the bi-quartic harmonic surfaces. Numerical experiments are visualized and presented to illustrate and support our results.