A numerical method for computing minimal surfaces in arbitrary dimension

In this paper we propose a numerical method for computing minimal surfaces with fixed boundaries. The level set method is used to evolve a codimension-1 surface with fixed codimension-2 boundary in R n under mean curvature flow. For n = 3 the problem has been approached in D.L. Chopp, 1993 and L.-T. Cheng [D.L. Chopp, Computing minimal surfaces via level set curvature flow, J. Comput. Phys. 106(1) (1993) 77–91 and L.-T. Cheng, The level set method applied to geometrically based motion, materials science, and image processing, UCLA CAM Report, 00-20] using the level set method, but with a more complicated boundary conditions. The method we present can be generalized straightforward to arbitrary dimension, and the framework in which it is presented is dimension independent. Examples are shown for n = 2, 3, 4.