Riemann-Schwarz Reflection Principle and Asymptotics of Modules of Rectangular Frames

TL;DR

This paper studies how the conformal module of a domain formed by two similar rectangles changes under stretching, providing insights into the asymptotic behavior and answering a question posed by Prof. Vuorinen.

Contribution

It introduces a new analysis of the asymptotics of conformal modules for rectangular frames under stretching, applying the Riemann-Schwarz reflection principle.

Findings

Derived asymptotic formulas for the conformal module under stretching.

Provided a solution to a question posed by Prof. Vuorinen.

Enhanced understanding of conformal invariants in rectangular domains.

Abstract

We investigate asymptotical behavior of the conformal module of a doubly-connected domain which is the difference of two homothetic rectangles under stretching it along the abscissa axis. Thereby, we give the answer to a question put by Prof. M.Vuorinen.