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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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참고문헌 (16)
참고문헌 신청
FRANÇOIS BERTELOOT / 2012 / Characterization of models in C2 by their automorphism groups / International Journal of Mathematics 05(05):619~634
Diganta Borah / 2020 / Boundary behavior of the Carathéodory and Kobayashi–Eisenman volume elements / Illinois Journal of Mathematics 64(2):151~168
Sanghyun Cho / 1994 / Boundary Behavior of the Bergman Kernel Function on some Pseudoconvex Domains in ℂ n / Transactions of the American Mathematical Society 345(2):803~817
Fusheng Deng / 2012 / Some properties of squeezing functions on bounded domains / Pacific Journal of Mathematics 257(2):319~341
F. Deng / 2016 / Properties of squeezing functions and global transformations of bounded do-mains / Trans. Amer. Math. Soc 368(4):2679~2696
Diganta Borah / 2020 / Boundary behavior of the Carathéodory and Kobayashi–Eisenman volume elements / Illinois Journal of Mathematics 64(2):151~168
Sanghyun Cho / 1994 / Boundary Behavior of the Bergman Kernel Function on some Pseudoconvex Domains in ℂ n / Transactions of the American Mathematical Society 345(2):803~817
Fusheng Deng / 2012 / Some properties of squeezing functions on bounded domains / Pacific Journal of Mathematics 257(2):319~341
F. Deng / 2016 / Properties of squeezing functions and global transformations of bounded do-mains / Trans. Amer. Math. Soc 368(4):2679~2696
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