2 Notations and Analytical Preliminaries

Minimal surfaces bounded by a polygon ? IR q (q 2) correspond in a one-to-one mannner to the critical points of Shiiman's function. For arbitrary, but xed polygons this function was investigated numerically in 16]. The present work extends the results in 16] to classes of polygons ? = ?(), where varies in certain subsets of nite dimensional spaces the dimensions of depending on the number of vertices of the polygon ?. In the numerical part investigations on the bifurcation process of one-parameter families of polygonal approximations of three well-known contour families are presented.