Stable solutions to the abelian Yang--Mills--Higgs equations on $S^2$ and $T^2$
Differential Geometry
2020-07-22 v1 Analysis of PDEs
Abstract
We show under natural assumptions that stable solutions to the abelian Yang--Mills--Higgs equations on Hermitian line bundles over the round -sphere actually satisfy the vortex equations, which are a first-order reduction of the (second-order) abelian Yang--Mills--Higgs equations. We also obtain a similar result for stable solutions on a flat -torus. Our method of proof comes from the work of Bourguignon--Lawson concerning stable Yang--Mills connections on compact homogeneous -manifolds.
Cite
@article{arxiv.2007.10968,
title = {Stable solutions to the abelian Yang--Mills--Higgs equations on $S^2$ and $T^2$},
author = {Da Rong Cheng},
journal= {arXiv preprint arXiv:2007.10968},
year = {2020}
}