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Uniqueness in \(\mathcal E(X,\omega)\). (English) Zbl 1171.32024

Author’s abstract: We prove uniqueness for the Dirichlet problem for the complex Monge–Ampère equation on compact Kähler manifolds in the sense of probability measures vanishing on pluripolar sets. The proof uses the mass concentration technique due to Kolodziej coupled with inequalities for mixed Monge–Ampère measures and the comparison principle.

MSC:

32W20 Complex Monge-Ampère operators
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