On the numerical approximation and computation of minimal surface continua bounded by one-parameter families of polygonal contours

Abstract Minimal surfaces bounded by a polygon Γ ⊂ R q (q ≥ 2) correspond in a one-to-one manner to the critical points of Shiffman's function θ. For arbitrary, but fixed polygons this function was investigated numerically by Hinze (1996). The present work extends these results to classes of polygons Γ = Γ(α), where α varies in certain subsets of finite-dimensional spaces the dimensions of which depend on the number of vertices of the polygon Γ. In the numerical part, investigations on the bifurcation process of one-parameter families of polygonal approximations of three well-known contour families are presented.

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