Sharp bounds for the growth and distortion of the analytic part of convex K-quasiconformal harmonic mappings

TL;DR

This paper establishes precise bounds on how much the analytic part of convex K-quasiconformal harmonic mappings can grow or distort, enhancing understanding of their geometric behavior.

Contribution

It provides the first sharp bounds for the growth and distortion of the analytic component of convex K-quasiconformal harmonic mappings.

Findings

Derived sharp upper bounds for the growth of the analytic part.

Established sharp lower bounds for the distortion of the analytic part.

Enhanced the theoretical understanding of convex K-quasiconformal harmonic mappings.

Abstract

The main aim of this paper is to obtain the sharp upper and lower bounds for the growth and distortion of the analytic part $h$ of sense-preserving convex $K$-quasiconformal harmonic mappings.