# Lengths, area and modulus of continuity of some classes of complex-valued functions

## TL;DR

This paper investigates the properties of complex-valued functions, focusing on their continuity, length, and area distortion, especially for solutions to Poisson's equation and K-quasiconformal mappings, extending classical results.

## Contribution

It extends classical results by providing bounds on length and area distortion for solutions to Poisson's equation and K-quasiconformal mappings.

## Key findings

- Bounds on length distortion for K-quasiconformal mappings
- Bounds on area distortion for solutions to Poisson's equation
- Extended classical results on modulus of continuity

## Abstract

In this paper, we discuss the modulus of continuity of solutions to Poisson's equation, and give bounds of length and area distortion for some classes of $K$-quasiconformal mappings satisfying Poisson's equations. The obtained results are the extension of the corresponding classical results.