# Numerical computation of Mityuk's function and radius for circular-radial slit domains

## TL;DR

This paper develops a numerical method using boundary integral equations to compute Mityuk's function and radius for multiply connected domains with circular and radial slits, validating theoretical properties.

## Contribution

It introduces a boundary integral equation approach for calculating Mityuk's function and radius in specific canonical domains, extending previous theoretical work.

## Key findings

- Validated the existence of critical points of Mityuk's radius.
- Demonstrated the boundary behavior of Mityuk's radius.
- Provided numerical results for domains with circular and radial slits.

## Abstract

We consider Mityuk's function and radius which have been proposed in \cite{Mit} as generalizations of the reduced modulus and conformal radius to the cases of multiply connected domains. We present a numerical method to compute Mityuk's function and radius for canonical domains that consist of the unit disk with circular/radial slits. Our method is based on the boundary integral equation with the generalized Neumann kernel. Special attention is given to the validation of the theoretical results on the existence of critical points and the boundary behavior of Mityuk's radius.