Mathematics

The study of area-minimizing surfaces in 3-space goes back to Euler. Interest in higher dimensions is, of course, more recent. After reviewing some of the history of area-minimizing surfaces in 3-space and some of the resulting examples of minimal surfaces, we will describe some of the difficulties involved in finding area-minimizing hypersurfaces computationally.

The least gradient method is a computational scheme for finding an approximation to a globally area-minimizing oriented hypersurface having a given boundary. The least gradient method avoids the difficulties alluded to above. The trade-off is that to obtain the best results and the best understanding the given boundary curve must lie
on the surface of a convex body.
Examples of applying the least gradient method
will be shown.