The Dirichlet Problem for Degenerate Complex Monge-ampere Equations
نویسنده
چکیده
The Dirichlet problem for a Monge-Ampère equation corresponding to a nonnegative, possible degenerate cohomology class on a Kähler manifold with boundary is studied. C1,α estimates away from a divisor are obtained, by combining techniques of Blocki, Tsuji, Yau, and pluripotential theory. In particular, C1,α geodesic rays in the space of Kähler potentials are constructed for each test configuration.
منابع مشابه
4 A ug 2 00 9 REGULARITY OF GEODESIC RAYS AND MONGE - AMPERE EQUATIONS 1
It is shown that the geodesic rays constructed as limits of Bergman geodesics from a test configuration are always of class C1,α, 0 < α < 1. An essential step is to establish that the rays can be extended as solutions of a Dirichlet problem for a Monge-Ampère equation on a Kähler manifold which is compact.
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