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arXiv · 1311.4948

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

Sebastien Picard
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Abstract

The regularity theory of the degenerate complex Monge-Ampère equation is studied. The equation is considered on a closed compact Kähler manifold $(M,g)$ with nonnegative orthogonal bisectional curvature of dimension $m$. Given a solution $ϕ$ of the degenerate complex Monge-Ampère equation $\det(g_{i \bar{j}} + ϕ_{i \bar{j}}) = f \det(g_{i \bar{j}})$, it is shown that the Laplacian of $ϕ$ can be controlled by a constant depending on $(M,g)$, $\sup f$, and $\inf_M Δf^{1/(m-1)}$.

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Sebastien Picard. 2013-11-20. A Priori Estimates of the Degenerate Monge-Ampere Equation on Kahler Manifolds of Nonnegative Bisectional Curvature. https://arxiv.org/abs/1311.4948

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