The complex Monge-Ampère operator in hyperconvex domains

Zbigniew Błocki

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Displaying similar documents to “The complex Monge-Ampère operator in hyperconvex domains”

Weak solutions to the complex Monge-Ampère equation on hyperconvex domains

Slimane Benelkourchi (2014)

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We show a very general existence theorem for a complex Monge-Ampère type equation on hyperconvex domains.

The Dirichlet problem for the degenerate Monge-Ampère equation.

Luis A. Caffarelli, Louis Nirenberg, Joel Spruck (1986)

Revista Matemática Iberoamericana

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Let Ω be a bounded convex domain in Rⁿ with smooth, strictly convex boundary ∂Ω, i.e. the principal curvatures of ∂Ω are all positive. We study the problem of finding a convex function u in Ω such that: det (u_ij) = 0 in Ω u = φ given on ∂Ω.

Regularity and Uniqueness of Solutions to Boundary Blow-up Problems for the Complex Monge-Ampère Operator

Björn Ivarsson (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

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We prove that plurisubharmonic solutions to certain boundary blow-up problems for the complex Monge-Ampère operator are Lipschitz continuous. We also prove that in certain cases these solutions are unique.

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.

An eigenvalue problem for the complex Monge-Ampère operator in pseudoconvex domains

N. D. Kutev, I. P. Ramadanov (1990)

Annales de l'I.H.P. Analyse non linéaire

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A unicity theorem for plurisubharmonic functions

Nguyen Quang Dieu (2011)

Annales Polonici Mathematici

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We give sufficient conditions for unicity of plurisubharmonic functions in Cegrell classes.

Weak solutions of equations of complex Monge-Ampère type

Sławomir Kołodziej (2000)

Annales Polonici Mathematici

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We prove some existence results for equations of complex Monge-Ampère type in strictly pseudoconvex domains and on Kähler manifolds.

Stability of Envelopes of Holomorphy and the Degenerate Monge-Ampère Equation.

Eric Bedford (1982)

Mathematische Annalen

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Weak solutions to the complex Hessian equation

Zbigniew Blocki (2005)

Annales de l’institut Fourier

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We investigate the class of functions associated with the complex Hessian equation ${(d d^{c} u)}^{m} \land ω^{n - m} = 0$ .

Counterexample to Regularity for the Complex Monge-Ampère Equation.

John Erik Fornaess, Eric Bedford (1978/79)

Inventiones mathematicae

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On the Dirichlet Problem for the Complex Monge-Ampère Operator.

Urban Cegrell (1984)

Mathematische Zeitschrift

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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.