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Sobolev Estimates for the Complex Monge-Ampère Operator on Complex Manifolds

Volume 16, Number 1 (2013), 55 - 58

Sobolev Estimates for the Complex Monge-Ampère Operator on Complex Manifolds

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Abstract

Solutions of the complex Monge-Amp\`ere Equation are obtained in the Sobolev topology on complex manifolds and through the Delta-Delta-Bar Lemma, in case the manifold is compact K\"ahler, a simple proof is given of the Aubin-Calabi-Yau Theorem.