On boundary points at which the squeezing function tends to one

TL;DR

This paper proves that in two complex dimensions, boundary points of smoothly bounded pseudoconvex domains with finite type are strictly pseudoconvex if the squeezing function approaches one, affirming a conjecture by Fornaess.

Contribution

It provides an affirmative answer to Fornaess's question in C^2 for domains with smooth finite type boundaries, linking the squeezing function limit to boundary pseudoconvexity.

Findings

Boundary points with squeezing function tending to one are strictly pseudoconvex in C^2.

Supports the conjecture relating the squeezing function limit to boundary geometry.

Establishes a connection between asymptotic squeezing behavior and boundary regularity.

Abstract

J. E. Fornaess has posed the question whether the boundary point of smoothly bounded pseudoconvex domain is strictly pseudoconvex, if the asymptotic limit of the squeezing function is 1. The purpose of this paper is to give an affirmative answer when the domain is in C^2 with smooth boundary of finite type in the sense of D'Angelo.