Displaying similar documents to “A result on the comparison principle for the log canonical threshold of plurisubharmonic functions”

A decomposition of complex Monge-Ampère measures

Yang Xing (2007)

Annales Polonici Mathematici

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We prove a decomposition theorem for complex Monge-Ampère measures of plurisubharmonic functions in connection with their pluripolar sets.

Monge-Ampère boundary measures

Urban Cegrell, Berit Kemppe (2009)

Annales Polonici Mathematici

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We study swept-out Monge-Ampère measures of plurisubharmonic functions and boundary values related to those measures.

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.

Subextension of plurisubharmonic functions without changing the Monge-Ampère measures and applications

Le Mau Hai, Nguyen Xuan Hong (2014)

Annales Polonici Mathematici

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The aim of the paper is to investigate subextensions with boundary values of certain plurisubharmonic functions without changing the Monge-Ampère measures. From the results obtained, we deduce that if a given sequence is convergent in C n - 1 -capacity then the sequence of the Monge-Ampère measures of subextensions is weakly*-convergent. As an application, we investigate the Dirichlet problem for a nonnegative measure μ in the class ℱ(Ω,g) without the assumption that μ vanishes on all pluripolar...

The general definition of the complex Monge-Ampère operator

Urban Cegrell (2004)

Annales de l’institut Fourier

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We define and study the domain of definition for the complex Monge-Ampère operator. This domain is the most general if we require the operator to be continuous under decreasing limits. The domain is given in terms of approximation by certain " test"-plurisubharmonic functions. We prove estimates, study of decomposition theorem for positive measures and solve a Dirichlet problem.

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.