Abstract
If G⊂⊂ℂnis pseudoconvex with smooth boundary and zo∈bG is a point_of finite type, one can ask the question: Does the Bergman kernel KG(z,¯z) grow like a rational power of dist(z,bG) when z approaches zo nontangentially? This question is suggested by observations for the domains Upg defined below. But the answer to this question is in general negative as is shown by a counterexample in ℂ3.
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Herbort, G. Logarithmic growth of the Bergman Kernel for weakly pseudoconvex domains in ℂ3 of finite type. Manuscripta Math 45, 69–76 (1983). https://doi.org/10.1007/BF01168581
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DOI: https://doi.org/10.1007/BF01168581