Vortex-type equations on compact Riemann surfaces. (English) Zbl 1535.53026
Summary: In this paper, we prove 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 [V. P. Pingali, Lett. Math. Phys. 110, No. 7, 1861–1875 (2020; Zbl 1442.53017)].
MSC:
| 53C07 | Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) |
| 70S15 | Yang-Mills and other gauge theories in mechanics of particles and systems |
| 30F10 | Compact Riemann surfaces and uniformization |
Citations:
Zbl 1442.53017References:
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