arXiv Analytics

Sign in

arXiv:2310.04866 [math.AP]AbstractReferencesReviewsResources

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

Aria Halavati

Published 2023-10-07, updated 2024-07-08Version 2

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. With the same method, we also prove the analogous second order stability for nearly minimizing pairs on nontrivial line bundles over arbitrary compact smooth surfaces.

Comments: Existing theorems on the Jacobian extended to multi vortex situation. Stability extended to compact surfaces. Style and cosmetic improvements
Categories: math.AP
Subjects: 35B35, 35Q56, 35Q40
Related articles: Most relevant | Search more
arXiv:math/0306108 [math.AP] (Published 2003-06-05, updated 2004-03-19)
Dispersive estimates for Schrodinger operators in dimensions one and three
arXiv:math/0101120 [math.AP] (Published 2001-01-13, updated 2002-02-20)
Almost optimal local well-posedness of the Maxwell-Klein-Gordon equations in 1+4 dimensions
arXiv:0807.0692 [math.AP] (Published 2008-07-04, updated 2009-09-14)
Global wellposedness and scattering for the defocusing energy-critical nonlinear Schrodinger equations of fourth order in dimensions $d\geq9$

Links

Toolbox