Stable solutions of $U(1)$ Yang-Mills-Higgs model in $\mathbb{R}^4$
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| Format: | Preprint |
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2024
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| _version_ | 1866912111272132608 |
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| author | Liu, Yong Wei, Juncheng Ye, Zikai |
| author_facet | Liu, Yong Wei, Juncheng Ye, Zikai |
| contents | We give a positive answer to the conjecture of Liu-Ma-Wei-Wu in \cite{LMWW} that the family of entire solutions to the $U(1)$-Yang-Mills-Higgs equation constructed by the gluing method in that paper are stable. This is the first family of examples of nontrivial stable critical points to the $U(1)$-Yang-Mills-Higgs model in higher dimensional Euclidean space. Intuitively, the stability of these solutions corresponds to the fact that holomorphic curves are area-minimizing. We also show that these entire solutions are non-degenerate. Our proof is based on detailed analysis of the linearized operators around this family and the spectrum estimates of the Jacobi operator by Arezzo-Pacard \cite{ArePac}. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_05447 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stable solutions of $U(1)$ Yang-Mills-Higgs model in $\mathbb{R}^4$ Liu, Yong Wei, Juncheng Ye, Zikai Analysis of PDEs Differential Geometry We give a positive answer to the conjecture of Liu-Ma-Wei-Wu in \cite{LMWW} that the family of entire solutions to the $U(1)$-Yang-Mills-Higgs equation constructed by the gluing method in that paper are stable. This is the first family of examples of nontrivial stable critical points to the $U(1)$-Yang-Mills-Higgs model in higher dimensional Euclidean space. Intuitively, the stability of these solutions corresponds to the fact that holomorphic curves are area-minimizing. We also show that these entire solutions are non-degenerate. Our proof is based on detailed analysis of the linearized operators around this family and the spectrum estimates of the Jacobi operator by Arezzo-Pacard \cite{ArePac}. |
| title | Stable solutions of $U(1)$ Yang-Mills-Higgs model in $\mathbb{R}^4$ |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2411.05447 |