论文标题
紧凑式Riemann表面上的涡旋型方程
Vortex-type equations on compact Riemann surfaces
论文作者
论文摘要
在本文中，我们证明了\ emph {a先验}估计紧凑型riemann表面上的某些涡流型方程。作为应用程序，我们恢复了涡旋束Monge-ampère方程的现有估计值，证明了Calabi-yang-mills方程的存在和独特定理，并获得了$ J- $ Vortex方程的估算。我们证明了与Gieseker稳定性以及几乎Hermitian Einstein指标的存在，即Kobayashi-Hitchin类型对应关系。我们还证明了在\ cite {vamsi3}中的calabi-yang-mills方程的矩形解释中产生的符号形式的kählerness。
In this paper, we prove \emph{a priori} estimates for some vortex-type equations on compact Riemann surfaces. As applications, we recover existing estimates for the vortex bundle Monge-Ampère equation, prove an existence and uniqueness theorem for the Calabi-Yang-Mills equations on vortex bundles, and get estimates for $J-$vortex equation. We prove an existence and uniqueness result relating Gieseker stability and the existence of almost Hermitian Einstein metrics, i.e., a Kobayashi-Hitchin type correspondence. We also prove Kählerness of the negative of the symplectic form which arises in the moment map interpretation of the Calabi-Yang-Mills equations in \cite{Vamsi3}
