On the growth of the Bergman kernel near an infinite-type point

Details On the growth of the Bergman kernel near an infinite-type point On the growth of the Bergman kernel near an infinite-type point

2007-08-21

arxiv.org/abs/0708.2894v2

Math. Ann. 347 (2010), 1-13

Mathematics

Complex Variables

Significant revisions made; simpler estimates; very mild strengthening of the hypotheses on Theorem 1.2 to get much stronger

Scientific paper

10.1007/s00208-009-0421-x

We study diagonal estimates for the Bergman kernels of certain model domains in $\mathbb{C}^2$ near boundary points that are of infinite type. To do so, we need a mild structural condition on the defining functions of interest that facilitates optimal upper and lower bounds. This is a mild condition; unlike earlier studies of this sort, we are able to make estimates for non-convex pseudoconvex domains as well. This condition quantifies, in some sense, how flat a domain is at an infinite-type boundary point. In this scheme of quantification, the model domains considered below range -- roughly speaking -- from being ``mildly infinite-type'' to very flat at the infinite-type points.

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