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

TL;DR

This paper investigates the existence and regularity of Coulomb frames in the normal bundle of 2D surfaces with higher codimension, providing new methods for codimensions greater than two and an a priori estimate for torsion coefficients.

Contribution

It introduces advanced techniques for establishing Coulomb frame existence in higher codimensions and offers an a priori estimate for torsion coefficients.

Findings

Existence of Coulomb frames in higher codimension cases.

Regularity results for Coulomb frames.

A priori estimates for torsion coefficients.

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.