For the complex Monge-Ampere eigenvalue problem on a strictly convex domain in C^2, the unique eigenfunction u satisfies that -log(-u) is strictly convex.
A microscopic convexity principle for nonlinear partial differential equations.Invent
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The log-concavity of eigenfunction to complex Monge-Amp\`ere operator in $\mathbb{C}^2$
For the complex Monge-Ampere eigenvalue problem on a strictly convex domain in C^2, the unique eigenfunction u satisfies that -log(-u) is strictly convex.