The least spanning area of a knot and the optimal bounding chain problem
Proceedings of the twenty-seventh annual symposium on Computational geometry
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The numerical least area problem for oriented hypersurfaces seeks algorithms which approximate area-minimizing hypersurfaces spanning a given boundary in Euclidean n-dimensional space. A mathematical model and numerical implementation are presented for finding the solution to the general least area problem for oriented surfaces in Euclidean three-dimensional space. (The mathematical model is valid for hypersurfaces of arbitrary Euclidean n-dimensional spaces.) There are no a priori restrictions on either the topological complexity of the given boundary or the topological type of the surfaces considered. As an example which illustrates the power of the method, the algorithm is applied to a boundary consisting of a pair of square-shaped linked curves. The resulting numerical surface is compared with an actual physical area-minimizing spanning surface (soap film).