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A priori estimates for weak solutions of complex Monge-Ampère equations

Slimane Benelkourchi, Vincent Guedj, Ahmed Zeriahi (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let X be a compact Kähler manifold and ω be a smooth closed form of bidegree ( 1 , 1 ) which is nonnegative and big. We study the classes χ ( X , ω ) of ω -plurisubharmonic functions of finite weighted Monge-Ampère energy. When the weight χ has fast growth at infinity, the corresponding functions are close to be bounded. We show that if a positive Radon measure is suitably dominated by the Monge-Ampère capacity, then it belongs to the range of the Monge-Ampère operator on some class χ ( X , ω ) . This is done by establishing...

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