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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Boundary behavior of the Bergman kernel function on some pseudoconvex domains in $ {\bf C}\sp n$

Author: Sanghyun Cho
Journal: Trans. Amer. Math. Soc. 345 (1994), 803-817
MSC: Primary 32H10; Secondary 32H15
MathSciNet review: 1254189
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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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Keywords: Bergman kernel function, finite 1-type, plurisubharmonic functions
Article copyright: © Copyright 1994 American Mathematical Society

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