Stable solutions of $U(1)$ Yang-Mills-Higgs model in $\mathbb{R}^4$

Yong Liu; Juncheng Wei; Zikai Ye

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arXiv · 2411.05447

Stable solutions of $U(1)$ Yang-Mills-Higgs model in $\mathbb{R}^4$

Yong Liu·Juncheng Wei·Zikai Ye

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Abstract

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}.

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Yong Liu, Juncheng Wei, Zikai Ye. 2024-11-08. Stable solutions of $U(1)$ Yang-Mills-Higgs model in $\mathbb{R}^4$. https://arxiv.org/abs/2411.05447

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