Monge-Ampère operators on compact Kähler manifolds
Vincent Guedj, Ahmed Zeriahi
Abstract
We study the complex Monge-Amp\` ere operator on compact Kähler manifolds. We give a complete description of its range on the set of ω-plurisubharmonic functions with L2 gradient and finite self energy, generalizing to this compact setting results of U.Cegrell from the local pluripoltential theory. We give some applications to complex dynamics and to the existence of Kähler-Einstein metrics on singular manifolds.
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