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

Abstract

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.

arXiv commentSignificant revisions made; simpler estimates; very mild strengthening of the hypotheses on Theorem 1.2 to get much stronger conclusions than in ver.1. To appear in Math. Ann

Cited by in corpus (1)

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