Strong localization of invariant metrics

TL;DR

This paper provides a quantitative analysis of how invariant metrics like Kobayashi, Azukawa, Sibony, and the squeezing function localize near special boundary points in complex domains, with applications to pseudoconvex boundaries.

Contribution

It introduces a quantitative version of strong localization for these metrics and the squeezing function near boundary points, extending understanding of their boundary behavior.

Findings

Quantitative localization of invariant metrics near plurisubharmonic peak points.

Analysis of metric behavior near strictly pseudoconvex boundary points.

Weak localization results near plurisubharmonic antipeak boundary points.

Abstract

A quantitative version of strong localization of the Kobayashi, Azukawa and Sibony metrics, as well as of the squeezing function, near a plurisubharmonic peak boundary point of a domain in $\Bbb C^n$ is given. As an application, the behavior of these metrics near a strictly pseudoconvex boundary point is studied. A weak localization of the three metrics and the squeezing function is also given near a plurisubharmonic antipeak boundary point.