Regularity of certain sets in ${\Bbb C}^n$
Volume 82 / 2003
Annales Polonici Mathematici 82 (2003), 219-232
MSC: 32U15, 32U35.
DOI: 10.4064/ap82-3-3
Abstract
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.
