Estimate of the squeezing function for a class of bounded domains

TL;DR

This paper constructs specific bounded domains where the squeezing function approaches zero near certain boundary points, highlighting limitations in the uniform boundedness of the squeezing function.

Contribution

It introduces a class of bounded domains with boundary points where the squeezing function is not uniformly bounded from below.

Findings

Squeezing function can tend to zero near smooth pseudoconvex boundary points.

Demonstrates limitations of squeezing function estimates in certain domains.

Provides examples that challenge previous assumptions about uniform bounds.

Abstract

We construct a class of bounded domains, on which the squeezing function is not uniformly bounded from below near a smooth and pseudoconvex boundary point.