On estimates for complex Monge-Ampère equations
A PDE proof is provided for the sharp L^∞ estimates for the complex Monge-Ampère
equation that had required pluripotential theory before. The proof covers both cases of fixed …
equation that had required pluripotential theory before. The proof covers both cases of fixed …
On the constant scalar curvature Kähler metrics (II)—Existence results
X Chen, J Cheng - Journal of the American Mathematical Society, 2021 - ams.org
In this paper, we apply our previous estimates in Chen and Cheng [On the constant scalar
curvature Kähler metrics (I): a priori estimates, Preprint] to study the existence of cscK …
curvature Kähler metrics (I): a priori estimates, Preprint] to study the existence of cscK …
Fully non-linear elliptic equations on compact Hermitian manifolds
G Székelyhidi - Journal of Differential Geometry, 2018 - projecteuclid.org
We derive a priori estimates for solutions of a general class of fully non-linear equations on
compact Hermitian manifolds. Our method is based on ideas that have been used for …
compact Hermitian manifolds. Our method is based on ideas that have been used for …
Gauduchon metrics with prescribed volume form
G Székelyhidi, V Tosatti, B Weinkove - 2017 - projecteuclid.org
Acta Mathematica 2017.219.1.6 Page 1 Acta Math., 219 (2017), 181–211 DOI: 10.4310/ACTA.2017.v219.n1.a6
c 2017 by Institut Mittag-Leffler. All rights reserved Gauduchon metrics with prescribed volume …
c 2017 by Institut Mittag-Leffler. All rights reserved Gauduchon metrics with prescribed volume …
The J-equation and the supercritical deformed Hermitian–Yang–Mills equation
G Chen - Inventiones mathematicae, 2021 - Springer
In this paper, we prove that for any Kähler metrics ω _0 ω 0 and χ χ on M, there exists a
Kähler metric ω _ φ= ω _0+-1 ∂ ̄ ∂ φ> 0 ω φ= ω 0+-1∂∂¯ φ> 0 satisfying the J-equation …
Kähler metric ω _ φ= ω _0+-1 ∂ ̄ ∂ φ> 0 ω φ= ω 0+-1∂∂¯ φ> 0 satisfying the J-equation …
On the constant scalar curvature K\" ahler metrics, general automorphism group
X Chen, J Cheng - arXiv preprint arXiv:1801.05907, 2018 - arxiv.org
In this paper, we derive estimates for scalar curvature type equations with more singular
right hand side. As an application, we prove Donaldson's conjecture on the equivalence …
right hand side. As an application, we prove Donaldson's conjecture on the equivalence …
Nakai-Moishezon criterions for complex Hessian equations
J Song - arXiv preprint arXiv:2012.07956, 2020 - arxiv.org
The $ J $-equation proposed by Donaldson is a complex Hessian quotient equation on K\"
ahler manifolds. The solvability of the $ J $-equation is proved by Song-Weinkove to be …
ahler manifolds. The solvability of the $ J $-equation is proved by Song-Weinkove to be …
A class of curvature type equations
P Guan, X Zhang - arXiv preprint arXiv:1909.03645, 2019 - arxiv.org
In this paper, we study the solvability of a general class of fully nonlinear curvature
equations, which can be viewed as generalizations of the equations for Christoffel …
equations, which can be viewed as generalizations of the equations for Christoffel …
K-stability for K\" ahler Manifolds
R Dervan, J Ross - arXiv preprint arXiv:1602.08983, 2016 - arxiv.org
We formulate a notion of K-stability for K\" ahler manifolds, and prove one direction of the
Yau-Tian-Donaldson conjecture in this setting. More precisely, we prove that the Mabuchi …
Yau-Tian-Donaldson conjecture in this setting. More precisely, we prove that the Mabuchi …
The deformed Hermitian-Yang-Mills equation in geometry and physics
We provide an introduction to the mathematics and physics of the deformed Hermitian–Yang–
Mills equation, a fully non-linear geometric PDE on Kähler manifolds which plays an …
Mills equation, a fully non-linear geometric PDE on Kähler manifolds which plays an …