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Continuity of singular Kähler-Einstein potentials

Continuity of singular Kähler-Einstein potentials

In this note, we investigate some regularity aspects for solutions of degenerate complex Monge-Ampere equations (DCMAE) on singular spaces. First, we study the Dirichlet problem for DCMAE on singular Stein spaces, showing a general continuity result. A consequence of our results is that Kahler-Einstein potentials are continuous at isolated singularities. …