Analytic discs, global extremal functions and projective hulls in projective space

Abstract

Using a recent result of Lárusson and Poletsky regarding plurisubharmonic subextensions, we prove a disc formula for the quasiplurisubharmonic global extremal function for domains in $\mathbb{P}^{n}$. As a corollary, we get a characterization of the projective hull for connected compact sets in $\mathbb{P}^{n}$ by the existence of analytic discs.