The Dirichlet problem for degenerate complex Monge–Ampere equations

Abstract

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