Monge-Ampère operators on compact Kähler manifolds

Details Monge-Ampère operators on compact Kähler manifolds Monge-Ampère operators on compact Kähler manifolds

2005-04-12

arxiv.org/abs/math/0504234v2

Mathematics

Complex Variables

29 pages, We show how to extend the results of the previous version to arbitrary dimension and indicate some applications

Scientific paper

We study the complex Monge-Amp\` ere operator on compact K\"ahler manifolds. We give a complete description of its range on the set of $\omega-$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 K\"ahler-Einstein metrics on singular manifolds.

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