Geodesic
Regularity of certain sets in ${\Bbb C}^n$
Nguyen Quang Dieu1
1 Department of Mathematics University of Education of Hanoi (Dai Hoc Su Pham Hanoi) Cau Giay, Tu Liem, Hanoi, Vietnam
Annales Polonici Mathematici, Tome 82 (2003) no. 3, pp. 219-232

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/ap82-3-3
Keywords: subset mathbb said regular sense pluripotential theory pluricomplex green function siciak extremal function continuous mathbb regular intersections sufficiently many complex lines regular subsets mathbb complete characterization regularity reinhardt sets given

Nguyen Quang Dieu 1

1 Department of Mathematics University of Education of Hanoi (Dai Hoc Su Pham Hanoi) Cau Giay, Tu Liem, Hanoi, Vietnam 
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Nguyen Quang Dieu. Regularity of certain sets in ${\Bbb C}^n$. Annales Polonici Mathematici, Tome 82 (2003) no. 3, pp. 219-232. doi: 10.4064/ap82-3-3

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