Carath\'eodory's Theorem and moduli of local connectivity

TL;DR

This paper provides a constructive proof of Carathéodory's Theorem using the concepts of local connectivity moduli and extremal distances of separating curves in annuli.

Contribution

It introduces a new constructive approach to Carathéodory's Theorem based on moduli of local connectivity and extremal distances.

Findings

Constructive proof of Carathéodory's Theorem

Use of moduli of local connectivity in complex analysis

Application of extremal distances to separating curves

Abstract

We give a constructive proof of the Carath\'eodory Theorem by means of the concept of a modulus of local connectivity and the extremal distance of the separating curves of an annulus.