\(C^{1,1}\) regularity of degenerate complex Monge-Ampère equations and some applications

DOI10.2140/apde.2021.14.1671zbMath1478.32122arXiv1807.06201OpenAlexW3197234452MaRDI QIDQ2236617

Jianchun Chu

Publication date: 25 October 2021

Published in: Analysis \& PDE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.06201

zbMATH Keywords

complex Monge-Ampère equation\(C^{1,1}\) estimatesalmost Hermitian manifolds

Mathematics Subject Classification ID

Degenerate elliptic equations (35J70) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Complex Monge-Ampère operators (32W20) Singular elliptic equations (35J75)

Related Items (1)

Fully non-linear degenerate elliptic equations in complex geometry

Cites Work

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• A variational approach to complex Monge-Ampère equations
• Regularity of the geodesic equation in the space of Sasakian metrics
• Estimates for the complex Monge-Ampère equation on Hermitian and balanced manifolds
• Monge-Ampère equations in big cohomology classes
• Regularity estimates of solutions to complex Monge-Ampère equations on Hermitian manifolds
• Regularity of envelopes in Kähler classes
• Potential theory on almost complex manifolds
• A gradient estimate in the Calabi-Yau theorem
• Quasiplurisubharmonic Green functions
• Existence and degeneration of Kähler-Einstein metrics on minimal algebraic varieties of general ype
• Some symplectic geometry on compact Kähler manifolds. I
• The Dirichlet problem for complex Monge-Ampère equations and regularity of the pluri-complex Green function
• The complex Monge-Ampère equation
• The space of Kähler metrics.
• On the \(C^{1,1}\) regularity of geodesics in the space of Kähler metrics
• Optimal regularity of plurisubharmonic envelopes on compact Hermitian manifolds
• Equations of Monge-Ampère type on compact Hermitian manifolds.
• The Monge-Ampère equation for non-integrable almost complex structures
• \(C^{1,1}\) regularity of geodesics in the space of volume forms
• Geodesics in the space of Kähler metrics
• Weak geodesics in the space of Kähler metrics
• On the Kähler-Ricci flow on projective manifolds of general type
• The Monge-Ampère equation on almost complex manifolds
• The weighted Monge-Ampère energy of quasiplurisubharmonic functions
• Complex Monge-Ampère equations and totally real submanifolds
• Smooth and Singular Kähler–Einstein Metrics
• Canonical measures and Kähler-Ricci flow
• Viscosity solutions to degenerate complex monge-ampère equations
• Singular Kähler-Einstein metrics
• Monge–Ampère Equations on Complex Manifolds with Boundary
• The complex Monge-Ampère equation on compact Hermitian manifolds
• The Space of Volume Forms
• Morse theory and geodesics in the space of Kähler metrics
• The dirichlet problem for nonlinear second-order elliptic equations. II. Complex monge-ampère, and uniformaly elliptic, equations
• Complex Monge-Ampere and Symplectic Manifolds
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
• C^1,1 regularity for degenerate complex Monge–Ampère equations and geodesic rays

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