The Dirichlet problem for the complex homogeneous Monge-Ampère equation

DOI10.1090/pspum/099/01744zbMath1448.32004arXiv1712.00405OpenAlexW2963273055MaRDI QIDQ5136625

Publication date: 27 November 2020

Published in: Proceedings of Symposia in Pure Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.00405

Mathematics Subject Classification ID

Kähler manifolds (32Q15) Boundary value problems on manifolds (58J32) Complex Monge-Ampère operators (32W20) Monge-Ampère equations (35J96) Flows related to complex manifolds (e.g., Kähler-Ricci flows, Chern-Ricci flows) (53E30)

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Envelopes with prescribed singularities ⋮ C1,1 regularity of geodesics of singular Kähler metrics

Cites Work

K-polystability of Q-Fano varieties admitting Kähler-Einstein metrics
Kiselman's principle, the Dirichlet problem for the Monge-Ampère equation, and rooftop obstacle problems
On a constant rank theorem for nonlinear elliptic PDEs
A variational approach to complex Monge-Ampère equations
Convexity on the space of Kähler metrics
A viscosity approach to degenerate complex Monge-Ampère equations
Classical and stochastic Laplacian growth
The Dirichlet problem for degenerate complex Monge-Ampère equations
Bergman metrics and geodesics in the space of Kähler metrics on toric varieties
Complex Monge-Ampère equations and geodesics in the space of Kähler metrics. Lecture notes
Perturbation theorems for Hele-Shaw flows and their applications
Calabi flow, geodesic rays, and uniqueness of constant scalar curvature Kähler metrics
Solving the degenerate complex Monge-Ampère equation with one concentrated singularity
A new capacity for plurisubharmonic functions
On a differential equation arising in a Hele Shaw flow moving boundary problem
Regularity of a boundary having a Schwarz function
Intrinsic capacities on compact Kähler manifolds
A uniqueness theorem in Kähler geometry
The Mabuchi geometry of finite energy classes
Harmonic discs of solutions to the complex homogeneous Monge-Ampère equation
Function theory in the unit ball of \({\mathbb{C}}^ n\)
Space of Kähler metrics. III: On the lower bound of the Calabi energy and geodesic distance
Quasiplurisubharmonic Green functions
Geometry of Kähler metrics and foliations by holomorphic discs
Mesures de Monge-Ampère et mesures pluriharmoniques. (Monge-Ampère measures and pluriharmonic measures)
Convex solutions of certain elliptic equations have constant rank Hessians
Some symplectic geometry on compact Kähler manifolds. I
The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian
Subharmonicity for uniform algebras
Potential methods in variational inequalities
The Dirichlet problem for a complex Monge-Ampère equation
The partial Legendre transformation for plurisubharmonic functions
The Dirichlet problem for complex Monge-Ampère equations and regularity of the pluri-complex Green function
A simplified proof for a moving boundary problem for Hele-Shaw flows in the plane
Hele-Shaw flow on hyperbolic surfaces
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
Envelopes of positive metrics with prescribed singularities
Optimal regularity of plurisubharmonic envelopes on compact Hermitian manifolds
Green functions with analytic singularities
The space of Kähler metrics. II.
A Cauchy integral approach to Hele-Shaw problems with a free boundary: The case of zero surface tension
Holomorphic discs and the complex Monge-Ampère equation.
Pluripotential theory. Lectures of the CIME course, Cetraro, Italy, 2011
Note on geodesic rays and simple test configurations
Quadrature identities and the Schottky double
Geodesics in the space of Kähler metrics
Weak geodesics in the space of Kähler metrics
Approximation of weak geodesics and subharmonicity of Mabuchi energy
Applications of the duality between the homogeneous complex Monge-Ampère equation and the Hele-Shaw flow
Toric partial density functions and stability of toric varieties
Hölder continuous solutions to Monge-Ampère equations
Test configurations for \(k\)-stability and geodesic rays
The Monge-Ampère operator and geodesics in the space of Kähler potentials
Analytic test configurations and geodesic rays
THE PLURICOMPLEX GREEN FUNCTION ON PSEUDOCONVEX DOMAINS WITH A SMOOTH BOUNDARY
Regularity of the pluricomplex Green function with several poles
The Hele-Shaw flow and moduli of holomorphic discs
Regularity of Plurisubharmonic Upper Envelopes in Big Cohomology Classes
Weak solutions to the complex Monge–Ampère equation
Regularity of geodesic rays and Monge-Ampère equations
Lectures on Stability and Constant Scalar Curvature
Nahm's equations and free-boundary problems
Extreme plurisubharmonic singularities
Morse theory and geodesics in the space of Kähler metrics
Intégration sur un ensemble analytique complexe
On a Generalized Dirichlet Problem for Plurisubharmonic Functions and Pseudo-Convex Domains. Characterization of Silov Boundaries
Relative types and extremal problems for plurisubharmonic functions
A Priori L -Estimates for Degenerate Complex Monge-Ampere Equations
Small modifications of quadrature domains
Bergman kernels and equilibrium measures for line bundles over projective manifolds
Extremal plurisubharmonic functions and invariant pseudodistances
The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
The dirichlet problem for nonlinear second-order elliptic equations. II. Complex monge-ampère, and uniformaly elliptic, equations
Applications of Variational Inequalities to a Moving Boundary Problem for Hele Shaw Flows
La métrique de Kobayashi et la représentation des domaines sur la boule
Complex Monge-Ampere and Symplectic Manifolds
Foliations and complex monge-ampère equations
On definitions of the pluricomplex Green function
Random polynomials with prescribed Newton polytope
An Introduction to Variational Inequalities and Their Applications
On the Optimal Regularity of Weak Geodesics in the Space of Metrics on a Polarized Manifold
The Bergman metric and the pluricomplex Green function
GREEN FUNCTIONS WITH SINGULARITIES ALONG COMPLEX SPACES
Plurisubharmonicity of envelopes of disc functionals on manifolds
Plurisubharmonic extremal functions, Lelong numbers and coherent ideal sheaves
Complex Legendre duality
Exponential Transforms, Resultants and Moments
Convexity of the 𝐾-energy on the space of Kähler metrics and uniqueness of extremal metrics
Regularity of Boundaries of Quadrature Domains in Two Dimensions
Test configurations and Geodesic rays
The pluricomplex Green function on some regular pseudoconvex domains
On the Regularity of the Pluricomplex Green Functions
Complex Monge Ampere Equations
Hele Shaw flows with a free boundary produced by the injection of fluid into a narrow channel
Hele-Shaw flow on weakly hyperbolic surfaces
The Siciak–Zahariuta extremal function as the envelope of disc functionals
The complex Monge-Ampère equation and pluripotential theory
The \(C^{1,1}\) regularity of the pluricomplex Green function
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