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Plurisubharmonic functions and potential theory in several complex variables. (English) Zbl 0962.31001

Pier, Jean-Paul (ed.), Development of mathematics 1950-2000. Basel: Birkhäuser. 655-714 (2000).
This is a history-oriented survey of the development of the theory of plurisubharmonic functions starting from their introduction by K. Oka [Tôhoku Math. J. 49, 15-52 (1942; Zbl 0060.24006)] and P. Lelong [C. R. Acad. Sci., Paris 215, 398-400 (1942; Zbl 0028.05601)] up to recent results in 1997. Every important application in potential theory in several complex variables during this period is presented in modern language, sometimes repeating beautiful original proofs and ideas. Just to mention a few of them: extremal functions, the complex Monge-Ampère operator, Lelong numbers and Green functions, pseudoconvex and Hartogs domains. The extensive references make the paper a very usable guide through the history and results of the theory of plurisubharmonic functions.
For the entire collection see [Zbl 0947.00008].

MSC:

31-02 Research exposition (monographs, survey articles) pertaining to potential theory
31C10 Pluriharmonic and plurisubharmonic functions
32U05 Plurisubharmonic functions and generalizations
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