Continuity of the relative extremal function on analytic varieties in $\Bbb{C}^n$
Volume 86 / 2005
Annales Polonici Mathematici 86 (2005), 219-225
MSC: Primary 32U15; Secondary 32B15.
DOI: 10.4064/ap86-3-2
Abstract
Let $V$ be an analytic variety in a domain $\mit\Omega \subset \Bbb {C}^n$ and let $K \subset\!\subset V$ be a closed subset. By studying Jensen measures for certain classes of plurisubharmonic functions on $V$, we prove that the relative extremal function $\omega_K$ is continuous on $V$ if $\mit\Omega$ is hyperconvex and $K$ is regular.
