Communications in Analysis and Geometry

Volume 18 (2010)

Number 1

The Dirichlet problem for degenerate complex Monge–Ampere equations

Pages: 145 – 170



D.H. Phong (Department of Mathematics, Columbia University)

Jacob Sturm (Department of Mathematics, Rutgers University)


The Dirichlet problem for a Monge–Ampère equationcorresponding to a non-negative, possible degeneratecohomology class on a Kähler manifold with boundary isstudied. $C^{1,\alpha}$ estimates away from a divisor areobtained, by combining techniques of Blocki, Tsuji, Yau and pluripotential theory. In particular, $C^{1,\alpha}$geodesic rays in the space of Kähler potentials areconstructed for each test configuration.

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