Stability and Hölder regularity of solutions to complex Monge-Ampère equations on compact Hermitian manifolds

DOI10.5802/aif.3436zbMath1487.32207arXiv2003.08417OpenAlexW3011639941MaRDI QIDQ2115496

Chinh H. Lu, Trong-Thuc Phung, Tat Dat Tô

Publication date: 17 March 2022

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.08417

zbMATH Keywords

stabilitycomparison principleHermitian manifoldcomplex Monge-Ampère equation

Mathematics Subject Classification ID

Kähler manifolds (32Q15) Complex Monge-Ampère operators (32W20) Plurisubharmonic functions and generalizations (32U05)

Related Items (5)

Continuous solutions to complex Hessian equations on Hermitian manifolds ⋮ Plurisigned hermitian metrics ⋮ Quasi-plurisubharmonic envelopes 3: solving Monge-Ampère equations on Hermitian manifolds ⋮ Complex geometry and dynamical systems. Abstracts from the workshop held September 4--10, 2022 ⋮ Families of singular Chern-Ricci flat metrics

Cites Work

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• The Kähler rank of compact complex manifolds
• Pluripotential theory on compact Hermitian manifolds
• A variational approach to complex Monge-Ampère equations
• Characterization of Monge-Ampère measures with Hölder continuous potentials
• Degenerate complex Monge-Ampère equations
• Monge-Ampère equations in big cohomology classes
• Pluripotential energy
• Regularity of envelopes in Kähler classes
• On the uniform estimate in the Calabi-Yau theorem. II
• Continuous solutions to Monge-Ampère equations on Hermitian manifolds for measures dominated by capacity
• The complex Monge-Ampère type equation on compact Hermitian manifolds and applications
• Hölder continuity of solutions to the complex Monge-Ampère equation with the right-hand side in \(L^{p}\): the case of compact Kähler manifolds
• On stability and continuity of bounded solutions of degenerate complex Monge-Ampère equations over compact Kähler manifolds
• Exponential estimates for plurisubharmonic functions
• An inequality for mixed Monge-Ampère measures
• Uniqueness in \(\mathcal E(X,\omega)\)
• The Dirichlet problem for a complex Monge-Ampère equation
• The complex Monge-Ampère equation
• On the existence of constant scalar curvature Kähler metric: a new perspective
• Monotonicity of nonpluripolar products and complex Monge-Ampère equations with prescribed singularity
• Optimal regularity of plurisubharmonic envelopes on compact Hermitian manifolds
• Stability and regularity of solutions of the Monge-Ampère equation on Hermitian manifolds
• Complex Monge-Ampère equation for measures supported on real submanifolds
• Log-concavity of volume and complex Monge-Ampère equations with prescribed singularity
• Stability of solutions to complex Monge-Ampère equations in big cohomology classes
• Hölder continuous solutions to Monge-Ampère equations
• On uniform estimate in Calabi-Yau theorem
• Complex Monge-Ampère equations and totally real submanifolds
• Volume and capacity of sublevel sets of a Lelong class of plurisubharmonic functions
• Weak solutions to the complex Monge-Amp\`ere equation on Hermitian manifolds
• Regularity of Plurisubharmonic Upper Envelopes in Big Cohomology Classes
• The complex Monge-Ampère equation on compact Hermitian manifolds
• Families of Monge-Ampère measures with Hölder continuous potentials
• Super-potentials for currents on compact Kähler manifolds and dynamics of automorphisms
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
• Monge-Ampere equation on compact Kahler manifolds
• On the singularity type of full mass currents in big cohomology classes
• Divisorial Zariski decompositions on compact complex manifolds
• Teichmuller Space is Not Gromov Hyperbolic
• On the constant scalar curvature Kähler metrics (II)—Existence results
• Geometric pluripotential theory on Kähler manifolds
• Pluripotential estimates on compact Hermitian manifolds
• Weak solutions of the Monge–Ampère equation on compact Hermitian manifolds
• Kähler-Einstein metrics on Fano manifolds. II: Limits with cone angle less than \boldmath2𝜋
• Hölder continuous solutions to Monge-Ampère equations

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