On Boundary Points at Which the Squeezing Function Tends to One

Abstract

J. E. Fornaess posed the question whether the boundary point of smoothly bounded pseudoconvex domain is strictly pseudoconvex, when the asymptotic limit value of the squeezing function is 1. The purpose of this paper is to give an affirmative answer if the domain is in $$\mathbb {C}^{2}$$ with smooth boundary of finite type in the sense of D’Angelo (Ann Math (2) 115(3):615–637, 1982).