Interior Regularity of Solutions to the Isotropically Constrained Plateau Problem

摘要

In this paper, we study the regularity of isotropically area-minimizing surfaces. We prove a partial regularity theorem which says that if an W~(1,2) isotropic map from a two-dimensional disk into R~(2n) minimizes area relative to its boundary among isotropic competitors and is close enough in WU2 norm to a linear holomor-phic isotropic nit.p, then it, is smooth in the interior. Furthermore, we prove that; the solution to the isotropically constrained Plateau problem exists and has a smooth interior with possibly isolated singularities.