On minimal surfaces with the same asymptotic curve in Euclidean space

摘要

In this paper, we approximate the minimal parametric surface with asymptotic curve by minimizing the Dirichlet function. The extremal of such a function can be easily computed as the solutions of linear systems, which avoid the high nonlinearity of the area function. They are not extremal of the area function but they are a fine approximation in some cases. Besides, an example to illustrate this method is given and plotted.