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Stable Abelian Yang--Mills--Higgs Fields on the Round Three-Sphere

  • Xishen Jin
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Abstract

We prove that every stable weak critical point of the self-dual abelian Yang--Mills--Higgs energy on the round three-sphere is gauge equivalent to the vacuum, for every positive scale parameter. This establishes the three-dimensional statement proposed by Cheng. For the non-stable critical point, we give a quantitative upper bound for the lowest eigenvalue of the Hessian on the gauge quotient.

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Cite

BibTeXRIS
BibTeX
@misc{jin2026stable,
  title = {{Stable Abelian Yang--Mills--Higgs Fields on the Round Three-Sphere}},
  author = {Xishen Jin},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.24045},
  eprint = {2609.24045},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.24045},
}
RIS
TY  - UNPB
TI  - Stable Abelian Yang--Mills--Higgs Fields on the Round Three-Sphere
AU  - Xishen Jin
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.24045
UR  - https://arxiv.org/abs/2609.24045
AB  - We prove that every stable weak critical point of the self-dual abelian Yang--Mills--Higgs energy on the round three-sphere is gauge equivalent to the vacuum, for every positive scale parameter. This establishes the three-dimensional statement proposed by Cheng. For the non-stable critical point, we give a quantitative upper bound for the lowest eigenvalue of the Hessian on the gauge quotient.
ER  -