A note on the boundary behaviour of the squeezing function and Fridman invariant

Abstract

Let $\Omega$ be a domain in ${\mathbb{C}}^n$. Suppose that $\partial \Omega$ is smooth pseudoconvex of D'Angelo finite type near a boundary point ${\xi }_0\in \partial \Omega$ and the Levi form has corank at most $1$ at ${\xi }_0$. Our goal is to show that if the squeezing function $s_{\Omega }({\eta }_j)$ tends to $1$ or the Fridman invariant $h_{\Omega }({\eta }_j)$ tends to $0$ for some sequence $\{{\eta }_j\}\subset \Omega$ converging to ${\xi }_0$, then this point must be strongly pseudoconvex.

References in corpus (2)

• Boundary behaviour of the Carathéodory and Kobayashi-Eisenman volume elements
• Some properties of $h$-extendible domains in ${\mathbb{C}}^{n+1}$