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

Bull. Korean Math. Soc. Published online July 14, 2020

Hyeseon Kim, Anh Duc Mai, Thi Lan Huong Nguyen, and Van Thu Ninh
Seoul National University, Tay Bac University, Hanoi University of Mining and Geology, Vietnam National University at Hanoi

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.

Keywords : holomorphic mappings, finite type domains, Fridman invariant, squeezing function