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

김혜선|Anh Duc Mai|Thi Lan Huong Nguyen|Van Thu Ninh
대한수학회 (The Korean Mathematical Society)|2020.09|대한수학회보 (Bulletin of the KMS)|제57권 제5호|pp. 1241-1249|DOI 10.4134/BKMS.b190913

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참고문헌

키워드

Finite type domainsFridman invariantholomorphic mappingssqueezing function
주제분류수학

초록

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.

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.

참고문헌 (16)

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