On the growth of the Bergman metric near a point of infinite type

Abstract

We derive optimal estimates for the Bergman kernel and the Bergman metric for certain model domains in ${\mathbb{C}}^2$ near boundary points that are of infinite type. Being unbounded models, these domains obey certain geometric constraints -- some of them necessary for a non-trivial Bergman space. However, these are mild constraints: unlike most earlier works on this subject, we are able to make estimates for non-convex pseudoconvex models as well. In fact, the domains we can analyse range from being mildly infinite-type to very flat at infinite-type boundary points.

arXiv comment16 pages; corrected a typo in v2 in the proof of Lemma 4.1; the final authenticated version of this is available online with the DOI mentioned here

References in corpus (1)

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