On the numerical approximation and computation of minimal surface continua bounded by one-parameter families of polygonal contours
A mapping \(u\in C^0(\overline B,\mathbb{R}^q)\cap C^2(B,\mathbb{R}^q)\) is called a disc-type minimal surface spanning \(\Gamma\) (Jordan curve in \(\mathbb{R}^q\)) if \(u\) satisfies \(\Delta u= 0\) and \(|u_{x_1}|^2-|u_{x_2}|^2= 0\) in \(B\), \(u|_{\partial B}\) is a (weakly) monotone parameterization of \(\Gamma\). For arbitrary, but fixed polygons \(\Gamma\) the corresponding Shiffman's function was studied numerically by the author [Numer. Math. 73, No. 1, 95-118 (1996; Zbl 0858.65060)]. In the present paper, these results are extended to classes of polygons \(\Gamma=\Gamma(\alpha)\), where \(\alpha\) varies in certain subsets of finite-dimensional spaces.
scientific article; zbMATH DE number 1072315
scientific article