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 .
Zbigniew Blocki (2005)
Annales de l’institut Fourier
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We investigate the class of functions associated with the complex Hessian equation .
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.
Kantorovich, L.V. (2004)
Journal of Mathematical Sciences (New York)
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Sławomir Kołodziej (1996)
Annales Polonici Mathematici
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We find a bounded solution of the non-homogeneous Monge-Ampère equation under very weak assumptions on its right hand side.
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.
Urban Cegrell (1984)
Mathematische Zeitschrift
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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.
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.
Machida, Y., Morimoto, T. (1999)
Lobachevskii Journal of Mathematics
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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.
Zbigniew Błocki (1996)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Urban Cegrell (2008)
Annales Polonici Mathematici
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We study a general Dirichlet problem for the complex Monge-Ampère operator, with maximal plurisubharmonic functions as boundary data.