Visible $\mathcal C^2$-smooth domains are pseudoconvex

TL;DR

This paper proves that domains with a certain geometric visibility property and smooth boundaries are necessarily pseudoconvex, linking geometric and complex analytic properties.

Contribution

It establishes a new connection between geometric visibility conditions and pseudoconvexity for smooth domains.

Findings

Visibility property implies pseudoconvexity for $ ext{C}^2$-smooth domains

Bridges geometric and complex analysis concepts

Provides a criterion for pseudoconvexity based on boundary smoothness and visibility

Abstract

We show that a domain that satisfies the visibility property with $\mathcal C^2$-smooth boundary is pseudoconvex.