Calculus of Variations and Geometric Measure Theory

A. Halavati

Quantitative stability of Yang-Mills-Higgs instantons in two dimensions

created by halavati on 10 Oct 2023


Submitted Paper

Inserted: 10 oct 2023
Last Updated: 10 oct 2023

Year: 2023

ArXiv: 2310.04866 PDF


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.