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

Bo Chen

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.

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

Abstract

This paper establishes decay estimates near isolated singularities for -dimensional Yang-Mills-Higgs fields defined on a fiber bundle (). 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.
Paper Structure (11 sections, 13 theorems, 102 equations)

This paper contains 11 sections, 13 theorems, 102 equations.

Table of Contents

  1. Introduction
  2. Yang-Mills-Higgs fields on a ball
  3. Backgrounds and main results
  4. Outline of the proof
  5. Preliminary
  6. Notations on bundles and equations for YMH fields
  7. Bochner formula and $\varepsilon$-regularity for YMH fields
  8. Kato inequalities for YMH fields
  9. Differential inequalities for YMH fields
  10. Decay estimates for YMH fields in higher dimensions
  11. The removability of singularities for YMH fields in higher dimensions

Key Result

Theorem 1.1

There exists an $\varepsilon_0$ such that if $(A,u)$ is a smooth YMH field on $B^*_1\subset \mathbb{R}^3$, which satisfies for some $R_0\leq 1$, then the singularity at the origin is removable.

Theorems & Definitions (21)

  • Theorem 1.1
  • Corollary 1.2
  • Theorem 1.3
  • Remark 1.4
  • Lemma 2.1
  • Theorem 2.2
  • Corollary 2.3
  • Proposition 2.4
  • Proposition 2.5
  • proof
  • ...and 11 more