A subset K of ℂⁿ is said to be regular in the sense of pluripotential theory if the pluricomplex Green function (or Siciak extremal function) is continuous in ℂⁿ. We show that K is regular if the intersections of K with sufficiently many complex lines are regular (as subsets of ℂ). A complete characterization of regularity for Reinhardt sets is also given.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap82-3-3,
author = {Nguyen Quang Dieu},
title = {Regularity of certain sets in Cn},
journal = {Annales Polonici Mathematici},
volume = {81},
year = {2003},
pages = {219-232},
zbl = {1066.32030},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap82-3-3}
}
Nguyen Quang Dieu. Regularity of certain sets in ℂⁿ. Annales Polonici Mathematici, Tome 81 (2003) pp. 219-232. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap82-3-3/