# The boundary behaviour of $K$-quasiconformal harmonic mappings

## TL;DR

This paper investigates the boundary behavior of $K$-quasiconformal harmonic mappings, focusing on their Lipschitz properties, measure distortion, and characterizations of radial John disks using Pre-Schwarzian derivatives.

## Contribution

It provides new characterizations of radial John disks and analyzes boundary behavior of $K$-quasiconformal harmonic mappings through Lipschitz and measure distortion properties.

## Key findings

- Established Lipschitz characteristics of $K$-quasiconformal harmonic mappings.
- Derived characterizations of radial John disks using Pre-Schwarzian derivatives.
- Analyzed linear measure distortion in the context of harmonic mappings.

## Abstract

In this article, we first discuss the Lipschitz characteristic and the linear measure distortion of $K$-quasiconformal harmonic mappings. Then we give some characterizations of the radial John disks with the help of Pre-Schwarzian of harmonic mappings.