A comparison principle for the complex Monge-Ampère operator in Cegrell’s classes and applications

In this article we will first prove a result about the convergence in capacity. Next we will obtain a general decomposition theorem for complex Monge-Ampère measures which will be used to prove a comparison principle for the complex Monge-Ampère operator.

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Veröffentlicht in:	Transactions of the American Mathematical Society 2009-10, Vol.361 (10), p.5539-5554
Hauptverfasser:	Khue, Nguyen Van, Hiep, Pham Hoang
Format:	Artikel
Sprache:	eng
Schlagworte:	Borel sets Complex Monge-Amp\`ere operator Dirichlet problem Exact sciences and technology General mathematics General, history and biography Greens function Mathematical functions Mathematical theorems Mathematics Perceptron convergence procedure plurisubharmonic function Research article Sciences and techniques of general use
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Zusammenfassung:	In this article we will first prove a result about the convergence in capacity. Next we will obtain a general decomposition theorem for complex Monge-Ampère measures which will be used to prove a comparison principle for the complex Monge-Ampère operator.
ISSN:	0002-9947 1088-6850 1088-6850
DOI:	10.1090/S0002-9947-09-04730-8