Asymptotics of Invariant Metrics in the normal direction and a new characterisation of the unit disk

TL;DR

This paper improves estimates of invariant metrics near the boundary of strictly pseudoconvex domains, providing a second-term expansion and a new characterization of the unit disk based on metric quotients.

Contribution

It introduces refined asymptotic expansions of invariant metrics and offers a novel characterization of the unit disk through metric quotient behavior.

Findings

Second-term expansion of invariant metrics in normal direction

Enhanced localization results for boundary estimates

New characterization of the unit disk via metric quotients

Abstract

We give improvements of estimates of invariant metrics in the normal direction on strictly pseudoconvex domains. Specifically we will give the second term in the expansion of the metrics. This depends on an improved localisation result and estimates in the one variable case. Finally we will give a new characterisation of the unit disk in $\mathbb C$ in terms of the asymptotic behaviour of quotients of invariant metrics.