Behavior of the squeezing function near h-extendible boundary points

TL;DR

This paper demonstrates that for smooth bounded pseudoconvex domains, the behavior of the squeezing function near an h-extendible boundary point indicates strict pseudoconvexity, linking geometric boundary properties with function behavior.

Contribution

It establishes a new criterion connecting the limit of the squeezing function to the strict pseudoconvexity at h-extendible boundary points.

Findings

Squeezing function tends to one at an h-extendible boundary point implies strict pseudoconvexity.

The result applies to $ ext{C}^ ext{infty}$-smooth, bounded pseudoconvex domains.

Provides a geometric characterization of boundary points via the squeezing function.

Abstract

It is shown that if the squeezing function tends to one at an h-extendible boundary point of a $\mathcal C^\infty$-smooth, bounded pseudoconvex domain, then the point is strictly pseudoconvex.