Existence of C... local Solutions for the Monge-Ampère equation.
J., Zuily, C. Hong (1987)
Inventiones mathematicae
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Displaying similar documents to “The Dirchlet Problem for a Complex Monge-Ampère Equation.”
Existence of C... local Solutions for the Monge-Ampère equation.
Counterexample to Regularity for the Complex Monge-Ampère Equation.
John Erik Fornaess, Eric Bedford (1978/79)
Inventiones mathematicae
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Global Hölder estimates for equations of Monge-Ampère type.
John I.E. Urbas (1988)
Inventiones mathematicae
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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.
On decomposable Monge-Ampère equations.
Machida, Y., Morimoto, T. (1999)
Lobachevskii Journal of Mathematics
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Geometry of the Complex Homogeneous Monge-Ampère Equation.
Pit-Mann Wong (1982)
Inventiones mathematicae
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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.
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.
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.
On formal theory of differential equations. II.
Jan Chrastina (1989)
Časopis pro pěstování matematiky
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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.