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Convergence in capacity

  • Yang Xing

    Publikation: Bidrag till tidskriftArtikel i vetenskaplig tidskriftPeer review

    Sammanfattning

    We study the relationship between convergence in capacities of plurisubharmonic functions and the convergence of the corresponding complex Monge-Ampere measures. We find one type of convergence of complex Monge-Ampbre measures which is essentially equivalent to convergence in the capacity C-n of functions. We also prove that weak convergence of complex Monge-Ampere measures is equivalent to convergence in the capacity Cn-1 of functions in some case. As applications we give certain stability theorems of solutions of Monge-Ampere equations.
    OriginalspråkEngelska
    Sidor (från-till)1839-1861
    Antal sidor24
    TidskriftAnnales de l'Institut Fourier
    Volym58
    Nummer5
    DOI
    StatusPublicerad - 2008

    Nyckelord

    • the complex Monge-Ampere operator
    • plurisubharmonic function
    • capacity

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