# Existence and characterisation of magnetic energy minimisers on oriented, compact Riemannian 3-manifolds with boundary in arbitrary helicity classes

## TL;DR

This paper investigates the existence, regularity, and properties of magnetic energy minimisers on compact Riemannian 3-manifolds with boundary, extending Arnold's classical results to more general settings.

## Contribution

It generalizes Arnold's results on magnetic energy minimization to arbitrary helicity classes on manifolds with boundary, providing new characterizations of minimisers.

## Key findings

- Existence of magnetic energy minimisers under helicity constraints
- Characterization of local and global minimisers
- Extension of Arnold's results to manifolds with boundary

## Abstract

In this paper we deal with the existence, regularity and Beltrami field property of magnetic energy minimisers under a helicity constraint. We in particular tackle the problem of characterising local as well as global minimisers of the given minimisation problem. Further we generalise Arnold's results concerning the problem of finding the minimum magnetic energy in an orbit of the group of volume-preserving diffeomorphisms to the setting of abstract manifolds with boundary.