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- W4287710532 abstract "We show under natural assumptions that stable solutions to the abelian Yang--Mills--Higgs equations on Hermitian line bundles over the round $2$-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 $2$-torus. Our method of proof comes from the work of Bourguignon--Lawson concerning stable $SU(2)$ Yang--Mills connections on compact homogeneous $4$-manifolds." @default.
- W4287710532 created "2022-07-26" @default.
- W4287710532 creator A5076266672 @default.
- W4287710532 date "2020-07-21" @default.
- W4287710532 modified "2023-10-16" @default.
- W4287710532 title "Stable solutions to the abelian Yang--Mills--Higgs equations on $S^2$ and $T^2$" @default.
- W4287710532 doi "https://doi.org/10.48550/arxiv.2007.10968" @default.
- W4287710532 hasPublicationYear "2020" @default.
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