Stable solutions of $U(1)$ Yang-Mills-Higgs model in $\mathbb{R}^4$
Analysis of PDEs
2024-11-11 v1 Differential Geometry
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 -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 -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}.
Keywords
Cite
@article{arxiv.2411.05447,
title = {Stable solutions of $U(1)$ Yang-Mills-Higgs model in $\mathbb{R}^4$},
author = {Yong Liu and Juncheng Wei and Zikai Ye},
journal= {arXiv preprint arXiv:2411.05447},
year = {2024}
}