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Uniqueness and stability for the complex Monge-Ampère equation on compact Kähler manifolds. (English) Zbl 1054.32024

We quote the author’s abstract: We prove uniqueness of weak solutions of the Dirichlet problem for the complex Monge-Ampère equation on compact Kähler manifolds. A qualitative version of this result implies the \(L^{2n/(n-1)} - L^{1}\) stability of solutions of this equation.

MSC:

32W20 Complex Monge-Ampère operators
32U15 General pluripotential theory
53C55 Global differential geometry of Hermitian and Kählerian manifolds
32J27 Compact Kähler manifolds: generalizations, classification
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