Pseudoconvexity is a two-dimensional phenomenon

TL;DR

This paper demonstrates that pseudoconvexity in complex n-dimensional space can be characterized entirely by examining its two-dimensional affine slices, simplifying the understanding of this property.

Contribution

It establishes that pseudoconvexity in C^n is equivalent to pseudoconvexity in all two-dimensional affine subspaces, providing a new geometric perspective.

Findings

Pseudoconvexity in C^n is determined by its two-dimensional intersections.

The characterization simplifies the analysis of pseudoconvexity.

The result bridges properties in higher dimensions with two-dimensional geometry.

Abstract

An open set in C^n is pseudoconvex if and only if its intersection with every affine subspace of complex dimension two as seen as an open set in C^2 is pseudoconvex.