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<p>In this paper, we derive decay estimates near isolated singularities of 3-dimensional (3d) Yang-Mills-Higgs fields defined on a fiber bundle, where the fiber is a compact Riemannian manifold instead of a vector space. As an application, we obtain removable singularity theorems for 3d Yang-Mills-Higgs fields under different types of energy conditions, which generalize classical removable singularity theorems for 3d (coupled) Yang-Mills fields and 3d harmonic maps. Our proof relies on a new improved Kato inequality for differential forms, which might be of independent interest.</p>

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Isolated singularities of 3-dimensional Yang-Mills-Higgs fields

  • 期刊论文

  • 发表日期：

    2026年5月19日

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  • Bo Chen,
  • Chong Song

摘要

In this paper, we derive decay estimates near isolated singularities of 3-dimensional (3d) Yang-Mills-Higgs fields defined on a fiber bundle, where the fiber is a compact Riemannian manifold instead of a vector space. As an application, we obtain removable singularity theorems for 3d Yang-Mills-Higgs fields under different types of energy conditions, which generalize classical removable singularity theorems for 3d (coupled) Yang-Mills fields and 3d harmonic maps. Our proof relies on a new improved Kato inequality for differential forms, which might be of independent interest.