Weak solutions to the complex Monge-Ampère equation on hyperconvex domains
We show a very general existence theorem for a complex Monge-Ampère type equation on hyperconvex domains.
A priori estimates for weak solutions of complex Monge-Ampère equations
Let be a compact Kähler manifold and be a smooth closed form of bidegree which is nonnegative and big. We study the classes of -plurisubharmonic functions of finite weighted Monge-Ampère energy. When the weight 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 . This is done by establishing...
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