Published Paper

Inserted: 10 oct 2023
Last Updated: 20 sep 2024

Journal: Arch. Rat. Mech. Anal.
Volume: 248
Number: 88
Year: 2023
Doi: https://doi.org/10.1007/s00205-024-02035-2

Abstract:

We prove that if an N-vortex pair nearly minimizes the Yang-Mills-Higgs energy, then it is second order close to a minimizer. First we use new weighted inequalities in two dimensions and compactness arguments to show stability for sections with some regularity. Second we define a selection principle using a penalized functional and by elliptic regularity and smooth perturbation of complex polynomials, we generalize the stability to all nearly minimizing pairs.