Continuity of plurisubharmonic envelopes

Nihat Gokhan Gogus

Annales Polonici Mathematici (2005)

  • Volume: 86, Issue: 3, page 197-217
  • ISSN: 0066-2216

Abstract

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Let D be a domain in ℂⁿ. The plurisubharmonic envelope of a function φ ∈ C(D̅) is the supremum of all plurisubharmonic functions which are not greater than φ on D. A bounded domain D is called c-regular if the envelope of every function φ ∈ C(D̅) is continuous on D and extends continuously to D̅. The purpose of this paper is to give a complete characterization of c-regular domains in terms of Jensen measures.

How to cite

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Nihat Gokhan Gogus. "Continuity of plurisubharmonic envelopes." Annales Polonici Mathematici 86.3 (2005): 197-217. <http://eudml.org/doc/280780>.

@article{NihatGokhanGogus2005,
abstract = {Let D be a domain in ℂⁿ. The plurisubharmonic envelope of a function φ ∈ C(D̅) is the supremum of all plurisubharmonic functions which are not greater than φ on D. A bounded domain D is called c-regular if the envelope of every function φ ∈ C(D̅) is continuous on D and extends continuously to D̅. The purpose of this paper is to give a complete characterization of c-regular domains in terms of Jensen measures.},
author = {Nihat Gokhan Gogus},
journal = {Annales Polonici Mathematici},
keywords = {plurisubharmonic envelopes; plurisubharmonic functions; -regular domains; Jensen measures; Jensen multifunctions; pluripotential theory; -regular boundaries; continuity of plurisubharmonic envelopes; Perron-Bremermann envelopes; Perron-Bremermann functions; strongly regular points},
language = {eng},
number = {3},
pages = {197-217},
title = {Continuity of plurisubharmonic envelopes},
url = {http://eudml.org/doc/280780},
volume = {86},
year = {2005},
}

TY - JOUR
AU - Nihat Gokhan Gogus
TI - Continuity of plurisubharmonic envelopes
JO - Annales Polonici Mathematici
PY - 2005
VL - 86
IS - 3
SP - 197
EP - 217
AB - Let D be a domain in ℂⁿ. The plurisubharmonic envelope of a function φ ∈ C(D̅) is the supremum of all plurisubharmonic functions which are not greater than φ on D. A bounded domain D is called c-regular if the envelope of every function φ ∈ C(D̅) is continuous on D and extends continuously to D̅. The purpose of this paper is to give a complete characterization of c-regular domains in terms of Jensen measures.
LA - eng
KW - plurisubharmonic envelopes; plurisubharmonic functions; -regular domains; Jensen measures; Jensen multifunctions; pluripotential theory; -regular boundaries; continuity of plurisubharmonic envelopes; Perron-Bremermann envelopes; Perron-Bremermann functions; strongly regular points
UR - http://eudml.org/doc/280780
ER -

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