Boundary behaviour of the complex Monge-Ampère equation
From MaRDI portal
Publication:1170437
DOI10.1007/BF02392727zbMath0496.35042OpenAlexW104894900MaRDI QIDQ1170437
John M. Lee, Richard B. Melrose
Publication date: 1982
Published in: Acta Mathematica (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf02392727
Degenerate elliptic equations (35J70) Partial differential equations on manifolds; differential operators (58J99) Pseudoconvex domains (32T99)
Related Items
Rigidity and gap theorems for Liouville's equation ⋮ The log term in the Bergman and Szegő kernels in strictly pseudoconvex domains in \(\mathbb C^2\) ⋮ Yang–Mills fields on CR manifolds ⋮ On the Dirichlet problem for the harmonic vector fields equation ⋮ On 3-dimensional CR manifolds and twistors ⋮ Plurisubharmonicity for the solution of the Fefferman equation and applications ⋮ \(Q\)-prime curvature on CR manifolds ⋮ Elliptic theory of differential edge operators I ⋮ Asymptotic expansions of complete Kähler-Einstein metrics with finite volume on quasi-projective manifolds ⋮ Holomorphic families of strongly pseudoconvex domains in a Kähler manifold ⋮ Large solutions to the Monge-Ampère equations with nonlinear gradient terms: existence and boundary behavior ⋮ Analytic continuation of weighted Bergman kernels ⋮ The Loewner-Nirenberg problem in singular domains ⋮ Kähler-Einstein metrics and obstruction flatness. II: Unit sphere bundles ⋮ Boundary behaviors for Liouville's equation in planar singular domains ⋮ Asymptotics of Kähler-Einstein metrics on complex hyperbolic cusps ⋮ Boundary regularity of minimal graphs in the hyperbolic space ⋮ On the asymptotic expansions of the proper harmonic maps between balls in Bergman metrics ⋮ Kähler-Einstein metrics and obstruction flatness of circle bundles ⋮ A nonlinear Poisson transform for Einstein metrics on product spaces ⋮ Smooth solutions of degenerate Laplacians on strictly pseudoconvex domains ⋮ Characteristic numbers of bounded domains ⋮ Optimal boundary regularity for nonlinear singular elliptic equations ⋮ Renormalized characteristic forms of the Cheng-Yau metric and global CR invariants ⋮ An integral formula for the $Q$-prime curvature in 3-dimensional CR geometry ⋮ Boundary behaviour of the Bergman invariant and related quantities ⋮ Analyse sur un demi-espace hyperbolique et poly-homogénéité locale ⋮ On the Szegő metric ⋮ Asymptotics of ACH-Einstein metrics ⋮ Version réelle de la conjecture de Ramadanov ⋮ An extension problem for the CR fractional Laplacian ⋮ Deformation of Einstein metrics and 𝐿² cohomology on strictly pseudoconvex domains ⋮ Resolvent of the Laplacian on strictly pseudoconvex domains ⋮ Polyhomogénéité des métriques asymptotiquement hyperboliques complexes le long du flot de Ricci ⋮ Self-dual solutions to pseudo Yang-Mills equations ⋮ On the scattering operators for ACHE metrics of Bergman type on strictly pseudoconvex domains ⋮ On expansions of Ricci flat ALE metrics in harmonic coordinates about the infinity ⋮ Toeplitz operators and weighted Bergman kernels ⋮ Canonical almost complex structures on ACH Einstein manifolds ⋮ Semi-isometric CR immersions of CR manifolds into Kähler manifolds and applications ⋮ Kähler-Einstein metrics on strictly pseudoconvex domains ⋮ A Burns-Epstein invariant for ACHE 4-manifolds ⋮ Pseudoharmonic maps and vector fields on \(CR\) manifolds ⋮ Asymptotics of complete Kähler metrics of finite volume on quasiprojective manifolds ⋮ The Webster scalar curvature and sharp upper and lower bounds for the first positive eigenvalue of the Kohn-Laplacian on real hypersurfaces ⋮ Local boundary regularity of the canonical Einstein-Kähler metric on pseudoconvex domains ⋮ Variation of total Q-prime curvature on CR manifolds ⋮ Estimate of the Einstein-Kähler metric on a weakly pseudoconvex domain in \(\mathbb{C}^ 2\) ⋮ Kähler-Einstein metrics with edge singularities ⋮ On the asymptotic expansion of complete Ricciflat Kähler metrics on quasi-projective manifolds ⋮ Boundary expansions of complete conformal metrics with negative Ricci curvatures ⋮ Approximately Einstein ACH metrics, volume renormalization, and an invariant for contact manifolds ⋮ Obstruction flat rigidity of the CR 3-sphere ⋮ Self-dual Einstein ACH metrics and CR GJMS operators in dimension three ⋮ Optimal global and boundary asymptotic behavior of large solutions to the Monge-Ampère equation ⋮ On the Kähler-Einstein metric at strictly pseudoconvex points ⋮ Optimal regularity of constant curvature graphs in hyperbolic space ⋮ Bounded strictly pseudoconvex domains in \(\mathbb{C}^2\) with obstruction flat boundary II ⋮ Contact harmonic maps ⋮ A boundary expansion of solutions to nonlinear singular elliptic equations ⋮ Boundary expansions for constant mean curvature surfaces in the hyperbolic space ⋮ Unnamed Item ⋮ On boundary behaviour of symplectomorphisms ⋮ CR invariants of weight five in the Bergman kernel ⋮ CR-HARMONIC MAPS ⋮ Boundary behavior of large solutions to the Monge-Ampère equations with weights ⋮ The moduli space of asymptotically cylindrical Calabi-Yau manifolds ⋮ Variations of Kähler-Einstein metrics on strongly pseudoconvex domains ⋮ The CR Ahlfors derivative and a new invariant for spherically equivalent CR maps
Cites Work
- Unnamed Item
- Transformation of boundary problems
- Monge-Ampère equations, the Bergman kernel, and geometry of pseudoconvex domains
- 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
This page was built for publication: Boundary behaviour of the complex Monge-Ampère equation