Magnetic bag like solutions to the SU(2) monopole equations on R^3

TL;DR

This paper constructs solutions to the SU(2) monopole equations resembling magnetic bags and proves bounds on their radii based on topological charge, advancing understanding of monopole configurations.

Contribution

It introduces explicit magnetic bag-like solutions to SU(2) monopole equations and provides rigorous bounds on their radii related to topological charge.

Findings

Constructed magnetic bag solutions matching conjectures

Proved bounds on solution radii based on topological charge

Enhanced understanding of monopole solution structures

Abstract

Solutions to the SU(2) monopole equations in the Bogolmony limit are constructed that look very much like Bolognesi's conjectured magnetic bag solutions. Three theorems are also stated and proved that give bounds in terms of the topological charge for the radii of balls where the solution's Higgs field has very small norm