Continuity of plurisubharmonic envelopes

Tom 86 / 2005

Nihat Gokhan Gogus Annales Polonici Mathematici 86 (2005), 197-217 MSC: Primary 32U15. DOI: 10.4064/ap86-3-1


Let $D$ be a domain in ${\mathbb{C}}^n$. The plurisubharmonic envelope of a function $\varphi \in C(\overline{D}{\hskip3.5pt I})$ is the supremum of all plurisubharmonic functions which are not greater than $\varphi$ on $D$. A bounded domain $D$ is called $c$-regular if the envelope of every function $\varphi \in C(\overline{D}{\hskip3.5pt I})$ is continuous on $D$ and extends continuously to $\overline{D}{\hskip3.5pt I}$. The purpose of this paper is to give a complete characterization of $c$-regular domains in terms of Jensen measures.


  • Nihat Gokhan GogusDepartment of Mathematics, 215 Carnegie Hall
    Syracuse University
    Syracuse, NY 13244, U.S.A.

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