Continuity of plurisubharmonic envelopes

Nihat Gokhan Gogus¹

¹ Department of Mathematics, 215 Carnegie Hall Syracuse University Syracuse, NY 13244, U.S.A.

Annales Polonici Mathematici, Tome 86 (2005) no. 3, pp. 197-217

Résumé

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.

Détail

DOI : 10.4064/ap86-3-1

Keywords: domain mathbb plurisubharmonic envelope function varphi overline hskip supremum plurisubharmonic functions which greater varphi bounded domain called regular envelope every function varphi overline hskip continuous extends continuously overline hskip purpose paper complete characterization c regular domains terms jensen measures