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arXiv · 2108.02754

Entire solutions of the magnetic Ginzburg-Landau equation in $\mathbb{R}^4$

Yong Liu·Xinan Ma·Juncheng Wei·Wangze Wu
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Abstract

We construct entire solutions of the magnetic Ginzburg-Landau equations in dimension 4 using Lyapunov-Schmidt reduction. The zero set of these solutions are close to the minimal submanifolds studied by Arezzo-Pacard\cite{Arezzo}. We also show the existence of a saddle type solution to the equations, whose zero set consists of two vertical planes in $\mathbb{R}^4$. These two types of solutions are believed to be energy minimizers of the corresponding energy functional and lie in the same connect component of the moduli space of entire solutions.

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Yong Liu, Xinan Ma, Juncheng Wei, Wangze Wu. 2021-08-05. Entire solutions of the magnetic Ginzburg-Landau equation in $\mathbb{R}^4$. https://arxiv.org/abs/2108.02754

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