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Monge-Ampère operators on compact Kähler manifolds

Vincent Guedj·Ahmed Zeriahi
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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 $L^2$ 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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Vincent Guedj, Ahmed Zeriahi. 2006-01-19. Monge-Ampère operators on compact Kähler manifolds. https://arxiv.org/abs/math/0504234

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