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arXiv · 1907.04528

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

Van Thu Ninh·Anh Duc Mai·Thi Lan Huong Nguyen·Hyeseon Kim
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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.

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Van Thu Ninh, Anh Duc Mai, Thi Lan Huong Nguyen, Hyeseon Kim. 2019-07-10. A note on the boundary behaviour of the squeezing function and Fridman invariant. https://arxiv.org/abs/1907.04528

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