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

Juncheng Wei; Wangze Wu; Xinan Ma; Yong Liu

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

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arxiv 2108.02754 v1 pith:ZKPPILSL submitted 2021-08-05 math.AP math.DG

Yong Liu , Xinan Ma , Juncheng Wei , Wangze Wu This is my paper · ORCID

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keywords solutionsentireenergyequationsginzburg-landaumagneticmathbbzero

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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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