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The J-equation and the supercritical deformed Hermitian–Yang–Mills equation

Gao Chen Institute of Geometry and Physics, University of Science and Technology of China, No.96 Jinzhai Road, Hefei, Anhui, China

Differential Geometry mathscidoc:2203.10004

Inventiones mathematicae, 225, 529-602, 2021.2
In this paper, we prove that for any Kähler metrics ω and χ on M, there exists a Kähler metric ω_φ = ω_0 + √-1 ∂ \bar∂ φ > 0 satisfying the J-equation tr_{ω_φ} χ = c if and only if (M, [ω0], [χ]) is uniformly J-stable. As a corollary, we find a sufficient condition for the existence of constant scalar curvature Kähler metrics with c_1 < 0. Using the same method, we also prove a similar result for the supercritical deformed Hermitian–Yang–Mills equation.
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@inproceedings{gao2021the,
  title={The J-equation and the supercritical deformed Hermitian–Yang–Mills equation},
  author={Gao Chen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220316114023830990983},
  booktitle={Inventiones mathematicae},
  volume={225},
  pages={529-602},
  year={2021},
}
Gao Chen. The J-equation and the supercritical deformed Hermitian–Yang–Mills equation. 2021. Vol. 225. In Inventiones mathematicae. pp.529-602. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220316114023830990983.
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