## Abstract

We consider the magnetic Ginzburg–Landau equations on a closed manifold (Formula presented.) (Formula presented.) formally corresponding to the Euler–Lagrange equations for the energy functional (Formula presented.) where (Formula presented.) and (Formula presented.) is a 1-form on (Formula presented.). Given a codimension-2 minimal submanifold (Formula presented.), which is also oriented and non-degenerate, we construct solutions (Formula presented.) such that (Formula presented.) has a zero set consisting of a smooth surface close to (Formula presented.). Away from (Formula presented.), we have (Formula presented.) as (Formula presented.), for all sufficiently small (Formula presented.) and (Formula presented.). Here, (Formula presented.) is a normal frame for (Formula presented.) in (Formula presented.). This improves a recent result by De Philippis and Pigati (2022), who built a solution for which the concentration phenomenon holds in an energy, measure-theoretical sense.

Original language | English |
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Article number | e12851 |

Journal | Journal of the London Mathematical Society |

Volume | 109 |

Issue number | 1 |

Early online date | 13 Jan 2024 |

DOIs | |

Publication status | Published - 31 Jan 2024 |

### Funding

The authors have been supported by Royal Society Research Professorship RP-R1-180114, United Kingdom. Marco Badran is grateful to Filippo Gaia, Jared Marx-Kuo, Alessandro Pigati and Bruno Premoselli for many useful comments and enlightening discussions related to some aspects of this work..

Funders | Funder number |
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Royal Society | RP-R1-180114 |

## ASJC Scopus subject areas

- General Mathematics