Regularity of certain sets in ${\Bbb C}^n$

Tom 82 / 2003

Nguyen Quang Dieu Annales Polonici Mathematici 82 (2003), 219-232 MSC: 32U15, 32U35. DOI: 10.4064/ap82-3-3

Streszczenie

A subset $K$ of ${{\mathbb C}}^n$ is said to be regular in the sense of pluripotential theory if the pluricomplex Green function (or Siciak extremal function) $V_K$ is continuous in ${{\mathbb C}}^n$. We show that $K$ is regular if the intersections of $K$ with sufficiently many complex lines are regular (as subsets of ${{\mathbb C}}$). A complete characterization of regularity for Reinhardt sets is also given.

Autorzy

  • Nguyen Quang DieuDepartment of Mathematics
    University of Education of Hanoi (Dai Hoc Su Pham Hanoi)
    Cau Giay, Tu Liem, Hanoi, Vietnam
    e-mail

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