Regularity of certain sets in ℂⁿ

Nguyen Quang Dieu. "Regularity of certain sets in ℂⁿ." Annales Polonici Mathematici 82.3 (2003): 219-232. <http://eudml.org/doc/280423>.

@article{NguyenQuangDieu2003,
abstract = {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) $V_K$ 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.},
author = {Nguyen Quang Dieu},
journal = {Annales Polonici Mathematici},
keywords = {plurisubharmonic functions; pluripotential theory; pluricomplex Green function, Siciak extremal function; regular set; locally regular set; Reinhardt set; Hartogs set.},
language = {eng},
number = {3},
pages = {219-232},
title = {Regularity of certain sets in ℂⁿ},
url = {http://eudml.org/doc/280423},
volume = {82},
year = {2003},
}

TY - JOUR
AU - Nguyen Quang Dieu
TI - Regularity of certain sets in ℂⁿ
JO - Annales Polonici Mathematici
PY - 2003
VL - 82
IS - 3
SP - 219
EP - 232
AB - 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) $V_K$ 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.
LA - eng
KW - plurisubharmonic functions; pluripotential theory; pluricomplex Green function, Siciak extremal function; regular set; locally regular set; Reinhardt set; Hartogs set.
UR - http://eudml.org/doc/280423
ER -