On the Schwarz Lemma for Bergman metrics of bounded domains

TL;DR

This paper introduces a new Schwarz Lemma applicable to bounded domains equipped with Bergman metrics, utilizing the Cauchy-Schwarz inequality from probability theory to establish the result.

Contribution

It provides a novel Schwarz Lemma for Bergman metrics on bounded domains, incorporating probabilistic inequalities into complex analysis.

Findings

Established a new Schwarz Lemma for Bergman metrics

Utilized the Cauchy-Schwarz inequality in the proof

Extended classical results to a broader class of domains

Abstract

We present a new Schwarz Lemma for bounded domains with Bergman metrics. The key ingredient of our proof is the Cauchy-Schwarz inequality from probability theory.