Quillen metrics and perturbed equations

Pingali, Vamsi Pritham

doi:10.1007/s11005-020-01279-9

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2020

2024

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Cited by 2 publications

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“…Solving the KYM equations in general, is quite challenging because they are of order four. Taking cue from the Calabi volume conjecture, Pingali [6] proposed to study the Calabi-Yang-Mills (CYM) equations as an easier toy model of the more complicated KYM equations and provided a moment map interpretation for them [8]. In [6], an openness result was proved for a special case of the CYM equations arising out of a vortex-type bundle.…”

Section: Introductionmentioning

confidence: 99%

Vortex-type equations on compact Riemann surfaces

Ghosh¹

2020

Preprint

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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, and prove an existence and uniqueness theorem for the Calabi-Yang-Mills equations on vortex bundles. We also prove an existence and uniqueness result relating Gieseker stability and the existence of almost Hermitian Einstein metrics, i.e., a Kobayashi-Hitchin type correspondence.

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Section: Introductionmentioning

confidence: 99%