A \(\mathcal{C}^{2, \alpha}\) estimate of the complex Monge-Ampère equation

DOI10.1016/j.jfa.2018.01.020zbMath1392.32019arXiv1705.08634OpenAlexW2793977707MaRDI QIDQ1753387

Xianqiang Yang

Publication date: 29 May 2018

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.08634

zbMATH Keywords

interior regularitycomplex Monge-Ampère equationinterior \(\mathcal{C}^{2, \alpha}\)-estimate

Mathematics Subject Classification ID

Complex Monge-Ampère operators (32W20)

Related Items (5)

Interior \(W^{2, p}\) estimate for small perturbations to the complex Monge-Ampère equation ⋮ Some interior regularity estimates for solutions of complex Monge-Ampère equations on a ball ⋮ On the constant scalar curvature Kähler metrics (I)—A priori estimates ⋮ Some new estimates for the complex Monge-Ampère equation ⋮ Local singularities of plurisubharmonic functions

Cites Work

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• \(C^{2,\alpha}\)-estimate for Monge-Ampère equations with Hölder-continuous right hand side
• \(C^{2,\alpha}\) regularities and estimates for nonlinear elliptic and parabolic equations in geometry
• Interior derivative estimates for the Kähler-Ricci flow
• \(C^{2,\alpha}\) estimates for nonlinear elliptic equations in complex and almost complex geometry
• Interior a priori estimates for solutions of fully nonlinear equations
• Regularity estimates of solutions to complex Monge-Ampère equations on Hermitian manifolds
• The complex Monge-Ampère equation on compact Kähler manifolds
• On Calabi's conjecture for complex surfaces with positive first Chern class
• A new capacity for plurisubharmonic functions
• Interior \(W^{2,p}\) estimates for solutions of the Monge-Ampère equation
• Hölder continuity of solutions to the complex Monge-Ampère equation with the right-hand side in \(L^{p}\): the case of compact Kähler manifolds
• Adiabatic limits of Ricci-flat Kähler metrics
• Uniqueness in \(\mathcal E(X,\omega)\)
• A priori estimates and a Liouville theorem for complex Monge-Ampère equations
• Kähler-Einstein metric on an open algebraic manifold
• Kähler-Einstein metrics on complex surfaces with \(C_ 1>0\)
• Complete Kähler manifolds with zero Ricci curvature. II
• The Dirichlet problem for a complex Monge-Ampère equation
• Kähler-Einstein metrics with positive scalar curvature
• The complex Monge-Ampère equation
• The space of Kähler metrics.
• Convergence of the Kähler-Ricci flow on noncompact Kähler manifolds
• Interior regularity of the complex Monge-Ampère equation in convex domains
• The extremal function associated to intrinsic norms.
• On the \(C^{2,\alpha}\)-regularity of the complex Monge-Ampère equation
• A correction to ``The Dirichlet problem for complex Monge-Ampère equations and regularity of the pluri-complex Green function
• Boundary regularity for the Monge-Ampère and affine maximal surface equations
• On the Kähler-Ricci flow on projective manifolds of general type
• On uniform estimate in Calabi-Yau theorem
• Schauder estimates for elliptic and parabolic equations
• Singular Kähler-Einstein metrics
• BOUNDEDLY NONHOMOGENEOUS ELLIPTIC AND PARABOLIC EQUATIONS
• On degenerate Monge-Ampere equations over closed Kahler manifolds
• Taming symplectic forms and the Calabi-Yau equation
• DEGENERATE COMPLEX MONGE–AMPÈRE EQUATIONS OVER COMPACT KÄHLER MANIFOLDS
• Fully Nonlinear, Uniformly Elliptic Equations Under Natural Structure Conditions
• The dirichlet problem for nonlinear second-order elliptic equations. II. Complex monge-ampère, and uniformaly elliptic, equations
• On the existence of solutions of a class of Monge-Ampére equations
• Variational Properties of the Complex Monge-Ampere Equation. II. Intrinsic Norms
• Classical solutions of fully nonlinear, convex, second-order elliptic equations
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
• On the existence of a complete Kähler metric on non-compact complex manifolds and the regularity of fefferman's equation
• The $\mathcal C^{2,\alpha}$ estimate of complex Monge-Ampere equation
• On the regularity of the complex Monge-Ampère equations
• Complete Kahler Manifolds with Zero Ricci Curvature. I

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