Displaying similar documents to “Geometry of the Complex Homogeneous Monge-Ampère Equation.”

Matrix inequalities and the complex Monge-Ampère operator

Jonas Wiklund (2004)

Annales Polonici Mathematici

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We study two known theorems regarding Hermitian matrices: Bellman's principle and Hadamard's theorem. Then we apply them to problems for the complex Monge-Ampère operator. We use Bellman's principle and the theory for plurisubharmonic functions of finite energy to prove a version of subadditivity for the complex Monge-Ampère operator. Then we show how Hadamard's theorem can be extended to polyradial plurisubharmonic functions.

The complex Monge-Ampère operator in the Cegrell classes

Rafał Czyż

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The complex Monge-Ampère operator is a useful tool not only within pluripotential theory, but also in algebraic geometry, dynamical systems and Kähler geometry. In this self-contained survey we present a unified theory of Cegrell's framework for the complex Monge-Ampère operator.

The complex Monge-Ampère equation for complex homogeneous functions in ℂⁿ

Rafał Czyż (2001)

Annales Polonici Mathematici

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We prove some existence results for the complex Monge-Ampère equation ( d d c u ) ⁿ = g d λ in ℂⁿ in a certain class of homogeneous functions in ℂⁿ, i.e. we show that for some nonnegative complex homogeneous functions g there exists a plurisubharmonic complex homogeneous solution u of the complex Monge-Ampère equation.