Further Developments of the Pluripotential Theory (Survey) View Full Text


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Chapter Info

DATE

2018-10-12

AUTHORS

Azimbay Sadullaev

ABSTRACT

It is well known that pluripotential theory, constructed in the 1980s, is based on plurisubharmonic (psh) functions and on the Monge-Ampe`re operator (ddcu)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≤m≤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. More... »

PAGES

167-182

References to SciGraph publications

  • 1994. Plurisubharmonic Functions in SEVERAL COMPLEX VARIABLES II
  • 2013-02. Capacities and Hessians in the class of m-subharmonic functions in DOKLADY MATHEMATICS
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  • 2012-12. Potential theory in the class of m-subharmonic functions in PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS
  • 1976-02. The dirichlet problem for a complex Monge-Ampère equation in INVENTIONES MATHEMATICAE
  • 2010-04. Plurisubharmonic functions in calibrated geometry and q-convexity in MATHEMATISCHE ZEITSCHRIFT
  • 1991-03. -problem on weaklyq-convex domains in MATHEMATISCHE ANNALEN
  • 2000-03. A criterion of algebraicity for Lelong classes and analytic sets in ACTA MATHEMATICA
  • 1980. P-regularity of sets in ¢n in ANALYTIC FUNCTIONS KOZUBNIK 1979
  • 1982-12. A new capacity for plurisubharmonic functions in ACTA MATHEMATICA
  • 1994. Convex Analysis and Nonlinear Geometric Elliptic Equations in NONE
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  • Book

    TITLE

    Algebra, Complex Analysis, and Pluripotential Theory

    ISBN

    978-3-030-01143-7
    978-3-030-01144-4

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-030-01144-4_14

    DOI

    http://dx.doi.org/10.1007/978-3-030-01144-4_14

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1107552181


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