Geodesic convexity of small neighborhood in the space of Kähler potentials

DOI10.1016/j.jfa.2020.108603zbMath1469.32016arXiv1805.02373OpenAlexW3023168696MaRDI QIDQ785840

Xiuxiong Chen, Mikhail Feldman, Jingchen Hu

Publication date: 12 August 2020

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

Full work available at URL: https://arxiv.org/abs/1805.02373

zbMATH Keywords

Riemann-Hilbert problemKähler potentialNash-Moser inverse function theoremdegenerate complex Monge-Ampère equation

Mathematics Subject Classification ID

Kähler manifolds (32Q15) Complex Monge-Ampère operators (32W20)

Related Items

An Obstacle for Higher Regularity of Geodesics in the Space of Kähler Potentials ⋮ Strict convexity of the Mabuchi functional for energy minimizers

Cites Work

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• The Cauchy problem for the homogeneous Monge-Ampère equation. III: Lifespan
• The imbedding problem for Riemannian manifolds
• Harmonic discs of solutions to the complex homogeneous Monge-Ampère equation
• Geometry of Kähler metrics and foliations by holomorphic discs
• An ontology of directional regularity implying joint regularity
• A remark on extremal Kähler metrics
• Some symplectic geometry on compact Kähler manifolds. I
• The boundary problems of physical geodesy
• Symplectic submanifolds and almost-complex geometry
• Scalar curvature and projective embeddings. I
• Elliptic partial differential equations of second order
• The space of Kähler metrics.
• On the maximal rank problem for the complex homogeneous Monge-Ampère equation
• On the \(C^{1,1}\) regularity of geodesics in the space of Kähler metrics
• Holomorphic discs and the complex Monge-Ampère equation.
• The Monge-Ampère equation for non-integrable almost complex structures
• Geodesics in the space of Kähler metrics
• Weak geodesics in the space of Kähler metrics
• Approximation of weak geodesics and subharmonicity of Mabuchi energy
• Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens
• The Hele-Shaw flow and moduli of holomorphic discs
• Regularity of the Dirichlet problem for the complex Monge-Ampère equation
• A NEW TECHNIQUE FOR THE CONSTRUCTION OF SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS
• On the Nash-Moser implicit function theorem
• Regularity of the dirichlet problem for the degenerate complex Monge-Ampère equation
• The inverse function theorem of Nash and Moser
• 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
• Convexity of the 𝐾-energy on the space of Kähler metrics and uniqueness of extremal metrics
• Kähler-Einstein metrics on Fano manifolds. I: Approximation of metrics with cone singularities

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