A note on the boundary behaviour of the squeezing function and Fridman invariant
Bull. Korean Math. Soc. 2020 Vol. 57, No. 5, 1241-1249
Published online September 30, 2020
Hyeseon Kim, Anh Duc Mai, Thi Lan Huong Nguyen, Van Thu Ninh
Seoul National University; Tay Bac University; Hanoi University of Mining and Geology; Thang Long Institute of Mathematics and Applied Sciences
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 : Finite type domains, Fridman invariant, holomorphic mappings, squeezing function
MSC numbers : Primary 32H02; Secondary 32M05, 32T25
Supported by : Part of this work was done while the authors were visiting the Vietnam Institute for Advanced Study in Mathematics (VIASM). They would like to thank the VIASM for financial support and hospitality. This research was supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2017.311 and the National Research Foundation of the Republic of Korea under grant number NRF-2018R1D1A1B07044363
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