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Continuity of the Complex Monge-Ampere Operator on Compact Kahler Manifolds

Yang Xing
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Abstract

We prove several approximation theorems of the complex Monge-Ampere operator on a compact Kahler manifold. As an application we give a new proof of a recent result of Guedj and Zeriahi on a complete description of the range of the complex Monge-Ampere operator in the class of w-plurisubharmonic functions with vanishing complex Monge-Ampere mass on all pluripolar sets. As a by-product we obtain a stability theorem of solutions of complex Monge-Ampere equations in some subclass.

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Yang Xing. 2007-04-09. Continuity of the Complex Monge-Ampere Operator on Compact Kahler Manifolds. https://arxiv.org/abs/math/0703755

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