The lower bound for the modulus of the derivatives and Jacobian of harmonic injective mappings

TL;DR

This paper establishes lower bounds for the derivatives and Jacobian of harmonic injective mappings from the unit ball onto convex domains, demonstrating their co-Lipschitz properties and reviewing related planar results with new insights.

Contribution

It provides new lower bounds for derivatives and Jacobian of harmonic injective mappings and explores their co-Lipschitz properties, including novel approaches in the planar case.

Findings

Lower bounds for radial derivatives and Jacobian established

Harmonic injective mappings are shown to be co-Lipschitz

Review of related planar results with new methods

Abstract

We give the lower bound for the modulus of the radial derivatives and Jacobian of harmonic injective mappings from the unit ball onto convex domain in plane and space. As an application we show co-Lipschitz property of some classes of qch mappings. We also review related results in planar case using some novelty.