Pluripotential Theory (London Mathematical Society Monographs New Series)

Pluripotential theory is a recently developed non-linear complex counterpart of classical potential theory. Its main area of application is multidimensional complex analysis. The central part of the pluripotential theory is occupied by maximal plurisubharmonic functions and the generalized complex Monge-Ampere operator. The interplay between these two concepts provides the focal point of this monograph, which contains an up-to-date account of the developments from the large volume of recent work in this area. A substantial proportion of the work is devoted to classical properties of subharmonic and plurisubharmonic functions, which makes the pluripotential theory available for the first time to a wide audience of analysts. The central part of the pluripotential theory is occupied by maximal plurisubharmonic functions and the generalized complex Monge-Ampere operator. The interplay between these two notions provides the focal point of this monograph, which explores classical properties of subharmonic and plurisubharmonic functions. Maciej Klimek. Includes Bibliographical References And Index.