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      A Priori Estimates of the Degenerate Monge-Ampere Equation on Kahler Manifolds of Nonnegative Bisectional Curvature

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          Abstract

          The regularity theory of the degenerate complex Monge-Amp\`{e}re equation is studied. The equation is considered on a closed compact K\"{a}hler manifold \((M,g)\) with nonnegative orthogonal bisectional curvature of dimension \(m\). Given a solution \(\phi\) of the degenerate complex Monge-Amp\`{e}re equation \(\det(g_{i \bar{j}} + \phi_{i \bar{j}}) = f \det(g_{i \bar{j}})\), it is shown that the Laplacian of \(\phi\) can be controlled by a constant depending on \((M,g)\), \(\sup f\), and \(\inf_M \Delta f^{1/(m-1)}\).

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          Most cited references 10

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          On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I

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            The dirichlet problem for a complex Monge-Amp�re equation

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              Monge–Ampère equations in big cohomology classes

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                Author and article information

                Journal
                19 November 2013
                Article
                1311.4948

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                To appear in Mathematical Research Letters
                math.AP math.CV

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