On the univalence criteria for elliptic polyharmonic and polyelliptic-harmonic mappings

TL;DR

This paper develops Landau-Bloch-type theorems and coefficient bounds for polyelliptic-harmonic mappings, advancing the understanding of their geometric and analytic properties with sharp results in certain cases.

Contribution

It introduces new Landau-Bloch-type theorems and coefficient bounds for polyelliptic-harmonic mappings, extending classical results to more complex elliptic polyharmonic contexts.

Findings

Established sharp Landau-Bloch-type theorems for poly $(K,K')$-elliptic harmonic mappings.

Derived coefficient bounds for $(K,K')$-elliptic and $K$-quasiregular polyharmonic mappings.

Provided applications of these bounds to Landau-Bloch-type theorems.

Abstract

In this paper, we first establish Landau-Bloch-type theorems for poly $(K,K')$-elliptic harmonic mappings, which are sharp in some given cases. Thereafter, we provide several coefficient bounds for $(K,K')$-elliptic and $K$-quasiregular polyharmonic mappings with bounded minimum distortion. Furthermore, using these coefficient bounds, we establish Landau-Bloch-type theorems for these mappings.