On a local characterization of pseudoconvex domains

TL;DR

This paper characterizes pseudoconvex domains in complex space using local conditions involving unbounded plurisubharmonic or holomorphic functions near boundary points.

Contribution

It provides a new local criterion for pseudoconvexity based on the existence of specific unbounded functions at boundary points.

Findings

Pseudoconvexity can be characterized locally by unbounded plurisubharmonic functions.

The criterion applies to boundary points in complex domains.

This approach offers a new perspective on the geometry of pseudoconvex domains.

Abstract

Pseudoconvexity of a domain in $\Bbb C^n$ is described in terms of the existence of a locally defined plurisubharmonic/holomorphic function near any boundary point that is unbounded at the point.