The least-gradient method for computing area minimizing hypersurfaces spanning arbitrary boundaries

In this paper we give a brief presentation of the least-gradient method. The least-gradient method is used to compute an approxination to a globally area minimizing oriented hypersurface having a given boundary, without the necessity of providing any a priori topological information about the area minimizing surface. The method has been successfully implemented. The first results were obtained, and published, for the case in which the boundary curve is required to lie on the surface of a convex body. Subsequent work has dealt with the general problem in which the given boundary curve is essentially unrestricted.