Matrix inequalities and the complex Monge-Ampère operator

Jonas Wiklund

Displaying similar documents to “Matrix inequalities and the complex Monge-Ampère operator”

On a problem of Monge.

Kantorovich, L.V. (2004)

Journal of Mathematical Sciences (New York)

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Subextension of plurisubharmonic functions without increasing the total Monge-Ampère mass

Rafał Czyż, Lisa Hed (2008)

Annales Polonici Mathematici

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We prove that subextension of certain plurisubharmonic functions is always possible without increasing the total Monge-Ampère mass.

A characterization of bounded plurisubharmonic functions

Pham Hoang Hiep (2005)

Annales Polonici Mathematici

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We give a characterization for boundedness of plurisubharmonic functions in the Cegrell class ℱ.

On decomposable Monge-Ampère equations.

Machida, Y., Morimoto, T. (1999)

Lobachevskii Journal of Mathematics

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A counterexample to the regularity of the degenerate complex Monge-Ampère equation

Szymon Pliś (2005)

Annales Polonici Mathematici

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We modify an example due to X.-J. Wang and obtain some counterexamples to the regularity of the degenerate complex Monge-Ampère equation on a ball in ℂⁿ and on the projective space ℙⁿ.

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.

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.

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

Slimane Benelkourchi (2014)

Annales Polonici Mathematici

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

On formal theory of differential equations. II.

Jan Chrastina (1989)

Časopis pro pěstování matematiky

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An energy estimate for the complex Monge-Ampère operator

Urban Cegrell, Leif Persson (1997)

Annales Polonici Mathematici

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We prove an energy estimate for the complex Monge-Ampère operator, and a comparison theorem for the corresponding capacity and energy. The results are pluricomplex counterparts to results in classical potential theory.