Geometric estimates for complex Monge-Ampère equations

DOI10.1515/crelle-2019-0020zbMath1447.35079arXiv1706.01527OpenAlexW2972659554MaRDI QIDQ2195126

Xin Fu, Jian Song, Bin Guo

Publication date: 7 September 2020

Published in: Journal für die Reine und Angewandte Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.01527

zbMATH Keywords

geometric regularity of singular solutionsuniform gradient and diameter estimates

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) A priori estimates in context of PDEs (35B45) Elliptic equations on manifolds, general theory (58J05) Monge-Ampère equations (35J96) PDEs on manifolds (35R01)

Related Items

The continuity equation of the Gauduchon metrics ⋮ Dirichlet problem for complex Monge–Ampère equation near an isolated KLT singularity ⋮ Calabi symmetry and the continuity method ⋮ Collapsing limits of the Kähler-Ricci flow and the continuity method ⋮ On the collapsing of Calabi-Yau manifolds and Kähler-Ricci flows ⋮ Diameter estimates for long-time solutions of the Kähler-Ricci flow ⋮ On \(L^{\infty}\) estimates for Monge-Ampère and Hessian equations on nef classes ⋮ Kähler-Einstein metrics near an isolated log-canonical singularity ⋮ On \(L^{\infty}\) estimate for complex Hessian quotient equations on compact Kähler manifolds ⋮ Geometry of twisted Kähler-Einstein metrics and collapsing ⋮ The continuity equation of almost Hermitian metrics ⋮ The continuity equation, Hermitian metrics and elliptic bundles ⋮ Kähler-Ricci flow on blowups along submanifolds ⋮ Local noncollapsing for complex Monge-Ampère equations

Cites Work

• Unnamed Item
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• A continuity method to construct canonical metrics
• Metric flips with Calabi ansatz
• Interior derivative estimates for the Kähler-Ricci flow
• The Kähler-Ricci flow through singularities
• Gromov-Hausdorff collapsing of Calabi-Yau manifolds
• The Dirichlet problem for degenerate complex Monge-Ampère equations
• Monge-Ampère equations in big cohomology classes
• On convexity of the regular set of conical Kähler-Einstein metrics
• Hölder continuity of solutions to the complex Monge-Ampère equation with the right-hand side in \(L^{p}\): the case of compact Kähler manifolds
• A uniform \(L^{\infty}\) estimate for complex Monge-Ampère equations
• Adiabatic limits of Ricci-flat Kähler metrics
• A gradient estimate in the Calabi-Yau theorem
• Pluricanonical systems on minimal algebraic varieties
• On Kähler-Einstein metrics on certain Kähler manifolds with \(C_ 1(M)>0\)
• On the structure of spaces with Ricci curvature bounded below. I
• The complex Monge-Ampère equation
• Contracting exceptional divisors by the Kähler-Ricci flow
• Collapsing of abelian fibered Calabi-Yau manifolds
• Hölder continuous solutions to Monge-Ampère equations
• The Kähler-Ricci flow on surfaces of positive Kodaira dimension
• Multiplier ideal sheaves and the Kähler-Ricci flow
• Canonical measures and Kähler-Ricci flow
• Regularity of Plurisubharmonic Upper Envelopes in Big Cohomology Classes
• Singular Kähler-Einstein metrics
• On degenerate Monge-Ampere equations over closed Kahler manifolds
• A Priori L -Estimates for Degenerate Complex Monge-Ampere Equations
• DEGENERATE COMPLEX MONGE–AMPÈRE EQUATIONS OVER COMPACT KÄHLER MANIFOLDS
• A General Schwarz Lemma for Kahler Manifolds
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
• The Kähler-Ricci flow, Ricci-flat metrics and collapsing limits
• Bounding Diameter Of Singular Kähler Metric
• On the structure of almost Einstein manifolds
• On Pointwise Gradient Estimates for the Complex Monge-Ampere Equation
• The Continuity Method on Minimal Elliptic Kähler Surfaces
• Contracting exceptional divisors by the Kähler-Ricci flow II