Boundary behavior of the Bergman kernel function on some pseudoconvex domains in 𝐶ⁿ

Cho, Sanghyun

doi:10.1090/S0002-9947-1994-1254189-7

Boundary behavior of the Bergman kernel function on some pseudoconvex domains in $\textbf {C}^ n$
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by Sanghyun Cho

Trans. Amer. Math. Soc. 345 (1994), 803-817

DOI: https://doi.org/10.1090/S0002-9947-1994-1254189-7

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Abstract:

Let $\Omega$ be a bounded pseudoconvex domain in ${\mathbb {C}^n}$ with smooth defining function r and let ${z_0} \in b\Omega$ be a point of finite type. We also assume that the Levi form $\partial \bar \partial r(z)$ of $b\Omega$ has $(n - 2)$-positive eigenvalues at ${z_0}$. Then we get a quantity which bounds from above and below the Bergman kernel function in a small constant and large constant sense.

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