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

## TL;DR

This paper provides optimal estimates for the Bergman kernel and metric near infinite-type boundary points in certain complex domains, including non-convex pseudoconvex models, expanding understanding of complex geometry in these settings.

## Contribution

It introduces new estimates for the Bergman kernel and metric on non-convex pseudoconvex domains at infinite-type boundary points, broadening previous results.

## Key findings

- Derived optimal estimates for Bergman kernel and metric
- Extended analysis to non-convex pseudoconvex models
- Applicable to domains with very flat infinite-type boundary points

## 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.