An Estimate for the Squeezing function and estimates of invariant metrics

TL;DR

This paper provides estimates for the squeezing function on strictly pseudoconvex domains and derives sharp boundary estimates for several invariant metrics, enhancing understanding of their behavior near domain boundaries.

Contribution

It introduces new boundary estimates for the squeezing function and invariant metrics on strictly pseudoconvex domains, advancing the theoretical understanding of these complex geometric objects.

Findings

Sharp boundary estimates for the squeezing function.

Precise boundary behavior of Caratheodory, Sibony, and Azukawa metrics.

Improved understanding of invariant metrics near domain boundaries.

Abstract

We give estimates for the squeezing function on strictly pseudoconvex domains, and derive some sharp estimates for the Caratheodory, Sibony and Azukawa metric near their boundaries.