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

@inproceedings{Liu2021EntireSO, title={Entire solutions of the magnetic Ginzburg-Landau equation in \$\mathbb\{R\}^4\$}, author={Yong Liu and Xinan Ma and Juncheng Wei and Wangze Wu}, year={2021} }

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[1]. We also show the existence of a saddle type solution to the equations, whose zero set consists of two vertical planes in R. 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…

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