Boundary behavior of the squeezing functions of $\mathbb C$-convex domains and plane domains

TL;DR

This paper investigates the boundary behavior of squeezing functions in complex convex domains, establishing uniform squeezing for non-degenerate $ ext{C}$-convex domains and analyzing the precise boundary behavior in plane domains with smoothness.

Contribution

It proves that all non-degenerate $ ext{C}$-convex domains are uniformly squeezing and characterizes the boundary behavior of the squeezing function in smooth plane domains.

Findings

Non-degenerate $ ext{C}$-convex domains are uniformly squeezing.

The boundary behavior of the squeezing function is precisely characterized near Dini-smooth boundary points.

Provides insights into the geometric structure of complex convex domains.

Abstract

It is shown that any non-degenerate $\mathbb C$-convex domain in $\mathbb C^n$ is uniformly squeezing. It is also found the precise behavior of the squeezing function near a Dini-smooth boundary point of a plane domain.