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arXiv · 2011.07268

Vortex-type equations on compact Riemann surfaces

Kartick Ghosh
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Abstract

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-Amp\`ere 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 K\"ahlerness of the negative of the symplectic form which arises in the moment map interpretation of the Calabi-Yang-Mills equations in \cite{Vamsi3}

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Kartick Ghosh. 2020-11-14. Vortex-type equations on compact Riemann surfaces. https://arxiv.org/abs/2011.07268

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