Abstract
We prove a C 1-estimate for the complex Monge–Ampère equation on a compact Kähler manifold directly from the C 0-estimate, without using a C 2-estimate. This was earlier done only under additional assumption of non-negative bisectional curvature.
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Partially supported by the projects N N201 3679 33 and 189/6 PR EU/2007/7 of the Polish Ministry of Science and Higher Education.