论文标题
Abelian Yang-Mills的稳定解决方案 - $ s^2 $和$ t^2 $上的higgs方程
Stable solutions to the abelian Yang--Mills--Higgs equations on $S^2$ and $T^2$
论文作者
论文摘要
我们在自然的假设下表明，在$ 2 $ -SPHERE上，对Hermitian线捆绑包的Abelian Yang-Mills方程稳定，实际上满足了涡旋方程，这是（二阶）Abelian Yang-Mills-Mills-Mills-Higgs-higgs-higgs方程的一阶减少。我们还获得了类似的结果，即在平坦的$ 2 $ torus上稳定解决方案。我们的证明方法来自Bourguignon-lawson关于稳定$ SU（2）$ Yang-Mills连接的工作，紧凑型同质$ 4 $ -Manifolds。
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.
