The Dirichlet problem for degenerate complex Monge-Ampere equations

Abstract

The Dirichlet problem for a Monge-Ampere equation corresponding to a nonnegative, possible degenerate cohomology class on a Kaehler manifold with boundary is studied. C^{1,α} estimates away from a divisor are obtained, by combining techniques of Blocki, Tsuji, Yau, and pluripotential theory. In particular, C^{1,α} geodesic rays in the space of Kaehler potentials are constructed for each test configuration

References in corpus (5)

• The Monge-Ampère operator and geodesics in the space of Kähler potentials
• Lectures on Stability and Constant Scalar Curvature
• Bergman metrics and geodesics in the space of Kähler metrics on toric varieties
• Singular Kahler-Einstein metrics
• Test configurations, large deviations and geodesic rays on toric varieties

Cited by in corpus (8)

• On the evolution of a Hermitian metric by its Chern-Ricci form
• The Monge-Ampère equation for (n-1)-plurisubharmonic functions on a compact Kähler manifold
• Conical Kahler-Einstein metric revisited
• Inoue surfaces and the Chern-Ricci flow
• Regularity of plurisubharmonic upper envelopes in big cohomology classes
• Deformed Hermitian-Yang-Mills Equation on Compact Hermitian Manifolds
• Hölder regularity of the solution to the complex Monge-Ampère equation with $L^p$ density
• Parabolic complex Monge-Ampère equations on compact Hermitian manifolds