  In this paper we consider the existence and regularity problem for Coulomb
frames in the normal bundle of two-dimensional surfaces with higher codimension
in Euclidean spaces. While the case of two codimensions can be approached
directly by potential theory, more sophisticated methods have to be applied for
codimensions greater than two. As an application we include an a priori
estimate for the corresponding torsion coefficients in arbitrary codimensions.
