# MathSciDoc: An Archive for Mathematician ∫

#### Differential Geometrymathscidoc: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.
@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.