On the existence of normal Coulomb frames for two-dimensional immersions with higher codimension

Abstract

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.