Weak closure of Singular Abelian $L^p$-bundles in $3$ dimensions

TL;DR

This paper establishes the weak closure property of a class of vector fields with integer flux in three dimensions, linking it to the minimization of the abelian Yang-Mills functional in higher dimensions.

Contribution

It proves the weak closure of singular Abelian L^p-bundles in 3D, connecting geometric measure theory with Yang-Mills minimization problems.

Findings

Weak sequential closure of vector fields with integer flux.

Connection to higher-dimensional abelian Yang-Mills minimization.

Foundational step for analyzing singular L^p-bundles in 3D.

Abstract

We prove the closure for the sequential weak $L^p$-topology of the class of vectorfields on $B^3$ having integer flux through almost every sphere. We show how this problem is connected to the study of the minimization problem for the Yang-Mills functional in dimension higher than critical, in the abelian case.