A reverse Schwarz--Pick inequality

TL;DR

This paper introduces a reverse form of the Schwarz--Pick inequality for holomorphic disk maps, providing new insights especially for inner functions and their derivatives.

Contribution

It establishes a novel reverse Schwarz--Pick inequality, enhancing understanding of inner functions and their derivative behavior.

Findings

Reverse Schwarz--Pick inequality proved for holomorphic self-maps

Clearer understanding of inner functions and derivatives

New perspective on holomorphic disk mappings

Abstract

We prove a kind of "reverse Schwarz--Pick lemma" for holomorphic self-maps of the disk. The result becomes especially clear-cut for inner functions and casts new light on their derivatives.