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The Dirichlet problem for the complex homogeneous Monge-Ampère equation

The Dirichlet problem for the complex homogeneous Monge-Ampère equation

We survey the Dirichlet problem for the complex Homogeneous Monge-Ampère Equation, both in the case of domains in C n and the case of compact Kähler manifolds parametrized by a Riemann surface with boundary.We then give a selfcontained account of previous work of the authors that connects this with the …