Analytic Discs, Global Extremal Functions and Projective Hulls in Projective Space

TL;DR

This paper establishes a disc formula for the global extremal function in complex projective space and characterizes the projective hull of compact sets via analytic discs, advancing understanding in complex geometry.

Contribution

It introduces a new disc formula for quasiplurisubharmonic extremal functions and characterizes projective hulls using analytic discs, based on recent plurisubharmonic subextension results.

Findings

Disc formula for quasiplurisubharmonic extremal functions

Characterization of projective hulls via analytic discs

Connection between extremal functions and geometric hulls

Abstract

Using a recent result of L\'arusson and Poletsky regarding plurisubharmonic subextensions we prove a disc formula for the quasiplurisubharmonic global extremal function for domains in complex projective space. As a corollary we get a characterization of the projective hull for connected compact sets in complex projective space by the existence of analytic discs.