A Schwarz-type lemma for squeezing function on planar domains

TL;DR

This paper proves a Schwarz-type lemma for the squeezing function on finitely connected planar domains, providing explicit formulas for doubly connected domains, enhancing understanding of conformal invariants.

Contribution

It introduces a new Schwarz-type lemma for squeezing functions on planar domains, simplifying derivations and extending previous results to more general settings.

Findings

Explicit formula for squeezing function on doubly connected domains

Schwarz-type lemma applicable to finitely connected planar domains

Simplified proof using maximum principle

Abstract

With an easy application of maximum principle, we establish a Schwarz-type lemma for squeezing function on finitely connected planar domains that directly yields the explicit formula for squeezing function on doubly connected domains obtained by Ng, Tang and Tsai.