Removable singularities of Yang-Mills-Higgs fields in higher dimensions

TL;DR

This paper proves decay estimates near isolated singularities for higher-dimensional Yang-Mills-Higgs fields, leading to a removable singularity theorem under energy bounds, extending classical results for related fields.

Contribution

It introduces decay estimates and a removable singularity theorem for Yang-Mills-Higgs fields in higher dimensions, generalizing known results for Yang-Mills and harmonic maps.

Findings

Decay estimates near singularities for $n$-dimensional Yang-Mills-Higgs fields

Removable singularity theorem under conformally invariant energy bounds

Extension of classical results to higher-dimensional settings

Abstract

This paper establishes decay estimates near isolated singularities for $n$-dimensional Yang-Mills-Higgs fields defined on a fiber bundle ($n \geq 4$). These estimates yield a removable singularity theorem for Yang-Mills-Higgs fields under conformally invariant energy bounds, extending the classical results for Yang-Mills fields and harmonic maps.