Communications in Analysis and Geometry
Volume 11 (2003)
Interior Regularity of Solutions to the Isotropically Constrained Plateau Problem
Pages: 945 – 986
In this paper, we study the regularity of isotropically areaminimizing surfaces. We prove a partial regularity theorem which says that if an W1,2 isotropic map from a two-dimensional disk into ℝ2n minimizes area relative to its boundary among isotropic competitors and is close enough in W1,2 norm to a linear holomorphic isotropic map, 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.