Further Developments of the Pluripotential Theory (Survey)

  • Azimbay SadullaevEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 264)


It is well known that pluripotential theory, constructed in the 1980s, is based on plurisubharmonic (psh) functions and on the Monge-Amp\(\grave{e}\)re operator \((dd^c u)^n\). In the 1990s there were many attempts to develop and expand pluripotential theory to broader classes such as the class of m-subharmonic \((m-sh)\) functions \((1\le m \le n)\). In this paper we will discuss some of the most important results of the theory of \(m-sh\) function as well as the difficulties and problems of constructing a potential theory in the class of \(m-sh\) functions.


Pluripotential theory Plurisubharmonic functions Operator Monge-Ampere Pluripolar sets M-subharmonic functions Maximal M-subharmonic functions 



I would like to express my warm thanks to the referee of this paper for numerous corrections and for witty simplification of the proof of Lemma 1, using Newton’s inequality.


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Authors and Affiliations

  1. 1.National University of UzbekistanTashkentUzbekistan

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